152:@0.053974:0.966765:0.079386:0.966765:0.079386:0.950778:0.053974:0.950778:0.000000:0.000000:0.000000
Interpretación geométrica del cociente :@0.404235:0.116974:0.894694:0.116974:0.894694:0.072315:0.404235:0.072315:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
incremental y de la derivada:@0.404235:0.154693:0.763372:0.154693:0.763372:0.110034:0.404235:0.110034:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
M.5.1.48. Interpretar de manera geométrica (pendiente de la secante) y física el cociente incremental (velocidad media) de funciones polinomiales de grado ≤4, con apoyo :@0.143847:0.925123:0.894325:0.925123:0.894325:0.915081:0.143847:0.915081:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de las TIC.:@0.143847:0.933924:0.188091:0.933924:0.188091:0.923882:0.143847:0.923882:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
M.5.1.51. Calcular de manera intuitiva la derivada de funciones racionales cuyos numeradores y denominadores sean polinomios de grado ≤2, para analizar la monotonía, :@0.143847:0.942726:0.894255:0.942726:0.894255:0.932683:0.143847:0.932683:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
determinar los máximos y mínimos de estas funciones y graficarlas con apoyo de las TIC (calculadora gráfica, software, applets). :@0.143847:0.951527:0.697092:0.951527:0.697092:0.941485:0.143847:0.941485:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Saberes previos:@0.199646:0.097890:0.307805:0.097890:0.307805:0.082418:0.199646:0.082418:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Cuál es la ecuación :@0.199884:0.126518:0.331862:0.126518:0.331862:0.111455:0.199884:0.111455:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cartesiana de la recta a partir de :@0.153341:0.142360:0.363399:0.142360:0.363399:0.127297:0.153341:0.127297:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
dos puntos dados? ¿Cuál es la :@0.153341:0.158202:0.348307:0.158202:0.348307:0.143139:0.153341:0.143139:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
pendiente de dicha recta?:@0.153341:0.174044:0.320514:0.174044:0.320514:0.158981:0.153341:0.158981:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Desequilibrio cognitivo:@0.199646:0.221195:0.363493:0.221195:0.363493:0.205723:0.199646:0.205723:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Cómo interpretas :@0.199884:0.249823:0.323557:0.249823:0.323557:0.234759:0.199884:0.234759:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
geométricamente a la derivada?:@0.153341:0.265665:0.358511:0.265665:0.358511:0.250601:0.153341:0.250601:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sean      [ ],      , fijo y      , tal que   ≠ 0. El grafo de la fun-:@0.404236:0.194905:0.891693:0.194905:0.891693:0.178407:0.404236:0.178407:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.442343:0.195021:0.446639:0.195021:0.446639:0.178552:0.442343:0.178552:0.000000
:@0.451475:0.194688:0.467523:0.194688:0.467523:0.180041:0.451475:0.180041:0.000000
P:@0.472743:0.195021:0.481528:0.195021:0.481528:0.178552:0.472743:0.178552:0.000000
4:@0.481552:0.198182:0.486505:0.198182:0.486505:0.188563:0.481552:0.188563:0.000000
:@0.492362:0.193818:0.505667:0.193818:0.505667:0.180956:0.492362:0.180956:0.000000
a:@0.518727:0.195021:0.527705:0.195021:0.527705:0.178552:0.518727:0.178552:0.000000
:@0.532155:0.194688:0.548203:0.194688:0.548203:0.180041:0.532155:0.180041:0.000000
:@0.553063:0.193818:0.566368:0.193818:0.566368:0.180956:0.553063:0.180956:0.000000
h:@0.612720:0.195021:0.622121:0.195021:0.622121:0.178552:0.612720:0.178552:0.000000
:@0.626610:0.194688:0.642658:0.194688:0.642658:0.180041:0.626610:0.180041:0.000000
:@0.647494:0.193818:0.660799:0.193818:0.660799:0.180956:0.647494:0.180956:0.000000
h:@0.721909:0.195021:0.731310:0.195021:0.731310:0.178552:0.721909:0.178552:0.000000
ción   es el conjunto definido como  ( ) = {( ,  ( ))} |      }.:@0.404244:0.212256:0.837206:0.212256:0.837206:0.195758:0.404244:0.195758:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.439287:0.212371:0.443583:0.212371:0.443583:0.195903:0.439287:0.195903:0.000000
G f:@0.661414:0.212371:0.683106:0.212371:0.683106:0.195903:0.661414:0.195903:0.000000:0.000000:0.000000
x f x:@0.719961:0.212371:0.752057:0.212371:0.752057:0.195903:0.719961:0.195903:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.783112:0.212371:0.790587:0.212371:0.790587:0.195903:0.783112:0.195903:0.000000
:@0.794729:0.212039:0.810777:0.212039:0.810777:0.197392:0.794729:0.197392:0.000000
:@0.815291:0.211169:0.828596:0.211169:0.828596:0.198307:0.815291:0.198307:0.000000
 :@0.404239:0.229606:0.408381:0.229606:0.408381:0.213109:0.404239:0.213109:0.000000
Consideramos dos puntos del grafo de  :   = ( ,  ( )), al que lo mante-:@0.404239:0.246957:0.891765:0.246957:0.891765:0.230459:0.404239:0.230459:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f P:@0.677973:0.247073:0.697186:0.247073:0.697186:0.230604:0.677973:0.230604:0.000000:0.000000:0.000000
0:@0.697185:0.250234:0.702139:0.250234:0.702139:0.240616:0.697185:0.240616:0.000000
a f a:@0.725643:0.247073:0.759973:0.247073:0.759973:0.230604:0.725643:0.230604:0.000000:0.000000:0.000000:0.000000:0.000000
nemos fijo, y   = (  +  ,  (  +  )), que variará conforme | | tienda (se :@0.404240:0.264308:0.895809:0.264308:0.895809:0.247810:0.404240:0.247810:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
P:@0.497792:0.264424:0.506577:0.264424:0.506577:0.247955:0.497792:0.247955:0.000000
a h f a h:@0.531622:0.264424:0.623710:0.264424:0.623710:0.247955:0.531622:0.247955:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
h:@0.803374:0.264424:0.812776:0.264424:0.812776:0.247955:0.803374:0.247955:0.000000
aproxime) a cero. Determinemos la ecuación cartesiana de la recta   :@0.404240:0.281659:0.895913:0.281659:0.895913:0.265161:0.404240:0.265161:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
L:@0.878626:0.281774:0.886467:0.281774:0.886467:0.265306:0.878626:0.265306:0.000000
h:@0.886290:0.285003:0.891771:0.285003:0.891771:0.275402:0.886290:0.275402:0.000000
que pasa por estos dos puntos. La ecuación cartesiana de la recta que :@0.404245:0.299009:0.896004:0.299009:0.896004:0.282512:0.404245:0.282512:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
pasa por los puntos   = ( ,  ( )) y   = (  +  ,  (  +  )) está definida :@0.404245:0.316360:0.895894:0.316360:0.895894:0.299863:0.404245:0.299863:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
P:@0.550468:0.316476:0.559253:0.316476:0.559253:0.300007:0.550468:0.300007:0.000000
0:@0.559271:0.319637:0.564224:0.319637:0.564224:0.310019:0.559271:0.310019:0.000000
a f a:@0.590231:0.316476:0.625834:0.316476:0.625834:0.300007:0.590231:0.300007:0.000000:0.000000:0.000000:0.000000:0.000000
P:@0.654808:0.316476:0.663593:0.316476:0.663593:0.300007:0.654808:0.300007:0.000000
a:@0.689602:0.316476:0.698579:0.316476:0.698579:0.300007:0.689602:0.300007:0.000000
h f a:@0.718634:0.316476:0.754699:0.316476:0.754699:0.300007:0.718634:0.300007:0.000000:0.000000:0.000000:0.000000:0.000000
h:@0.774754:0.316476:0.784155:0.316476:0.784155:0.300007:0.774754:0.300007:0.000000
como el conjunto de puntos que satisfacen la condición: ( ,  )    , :@0.404245:0.333711:0.895912:0.333711:0.895912:0.317213:0.404245:0.317213:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.817442:0.333827:0.839716:0.333827:0.839716:0.317358:0.817442:0.317358:0.000000:0.000000:0.000000
:@0.850004:0.333494:0.866052:0.333494:0.866052:0.318847:0.850004:0.318847:0.000000
:@0.870759:0.332624:0.884063:0.332624:0.884063:0.319762:0.870759:0.319762:0.000000
2:@0.884063:0.327358:0.889017:0.327358:0.889017:0.317740:0.884063:0.317740:0.000000
tal es que   –  ( ) =  ( )(  –  ), con   ≠ 0.:@0.404244:0.351062:0.704859:0.351062:0.704859:0.334564:0.404244:0.334564:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y f a:@0.476045:0.351177:0.521743:0.351177:0.521743:0.334709:0.476045:0.334709:0.000000:0.000000:0.000000:0.000000:0.000000
Q h x a:@0.546787:0.351177:0.621171:0.351177:0.621171:0.334709:0.546787:0.334709:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
h:@0.665115:0.351177:0.674516:0.351177:0.674516:0.334709:0.665115:0.334709:0.000000
Observamos que la pendiente de la recta es el cociente incremental  :@0.404244:0.385763:0.891081:0.385763:0.891081:0.369266:0.404244:0.369266:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Q h:@0.404244:0.410358:0.431485:0.410358:0.431485:0.393889:0.404244:0.393889:0.000000:0.000000:0.000000
( ) que se define como:  ( ) =                            ,   ≠ 0.:@0.416130:0.410242:0.799717:0.410242:0.799717:0.393745:0.416130:0.393745:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Q h:@0.588955:0.410358:0.616196:0.410358:0.616196:0.393889:0.588955:0.393889:0.000000:0.000000:0.000000
h:@0.759973:0.410358:0.769374:0.410358:0.769374:0.393889:0.759973:0.393889:0.000000
Luego, la ecuación cartesiana de la recta   se escribe como ( ,  )    ,:@0.404244:0.434721:0.891770:0.434720:0.891770:0.418222:0.404244:0.418224:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
L:@0.682735:0.434837:0.690576:0.434837:0.690576:0.418368:0.682735:0.418368:0.000000
h:@0.690262:0.438065:0.695743:0.438065:0.695743:0.428464:0.690262:0.428464:0.000000
x y:@0.820562:0.434836:0.841931:0.434836:0.841931:0.418367:0.820562:0.418367:0.000000:0.000000:0.000000
:@0.851352:0.434503:0.867400:0.434503:0.867400:0.419856:0.851352:0.419856:0.000000
:@0.871055:0.433633:0.884360:0.433633:0.884360:0.420771:0.871055:0.420771:0.000000
2:@0.884176:0.428368:0.889129:0.428368:0.889129:0.418750:0.884176:0.418750:0.000000
tal que   –  ( ) =                            (  –  ), con   ≠ 0.:@0.404244:0.459199:0.764986:0.459199:0.764986:0.442701:0.404244:0.442701:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y f a:@0.457531:0.459315:0.503229:0.459315:0.503229:0.442846:0.457531:0.442846:0.000000:0.000000:0.000000:0.000000:0.000000
x a:@0.646061:0.459315:0.681297:0.459315:0.681297:0.442846:0.646061:0.442846:0.000000:0.000000:0.000000
h:@0.725241:0.459315:0.734643:0.459315:0.734643:0.442846:0.725241:0.442846:0.000000
En la Figura 4.1., se muestran las :@0.404244:0.493901:0.635523:0.493901:0.635523:0.477403:0.404244:0.477403:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
posiciones de los puntos  ,  , :@0.404244:0.511251:0.635523:0.511252:0.635523:0.494754:0.404244:0.494754:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
P P:@0.592097:0.511367:0.623758:0.511368:0.623758:0.494899:0.592097:0.494898:0.000000:0.000000:0.000000
1:@0.600844:0.514529:0.605797:0.514529:0.605797:0.504910:0.600844:0.504910:0.000000
2:@0.623706:0.514529:0.628659:0.514529:0.628659:0.504910:0.623706:0.504910:0.000000
P P:@0.404244:0.528718:0.438073:0.528718:0.438073:0.512250:0.404244:0.512250:0.000000:0.000000:0.000000
3:@0.412963:0.531879:0.417916:0.531879:0.417916:0.522261:0.412963:0.522261:0.000000
,  , …, que corresponden a :@0.417883:0.528603:0.635527:0.528603:0.635527:0.512105:0.417883:0.512105:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
4:@0.438014:0.531879:0.442967:0.531879:0.442967:0.522261:0.438014:0.522261:0.000000
valores de   > 0 que tienden o :@0.404229:0.545953:0.635489:0.545953:0.635489:0.529456:0.404229:0.529456:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
h:@0.482523:0.546069:0.491924:0.546069:0.491924:0.529600:0.482523:0.529600:0.000000
se aproximan a 0. También se :@0.404229:0.563304:0.635525:0.563304:0.635525:0.546806:0.404229:0.546806:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
muestran las posiciones de las :@0.404229:0.580655:0.635508:0.580655:0.635508:0.564157:0.404229:0.564157:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
rectas :@0.404229:0.598006:0.450292:0.598006:0.450292:0.581508:0.404229:0.581508:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
L:@0.450851:0.598121:0.458692:0.598121:0.458692:0.581653:0.450851:0.581653:0.000000
h:@0.458646:0.601282:0.464273:0.601282:0.464273:0.591664:0.458646:0.591664:0.000000
(1):@0.460028:0.591656:0.471855:0.591656:0.471855:0.582038:0.460028:0.582038:0.000000:0.000000:0.000000
, :@0.471820:0.598006:0.478660:0.598006:0.478660:0.581508:0.471820:0.581508:0.000000:0.000000
L:@0.479218:0.598121:0.487059:0.598121:0.487059:0.581653:0.479218:0.581653:0.000000
h:@0.487008:0.601282:0.492635:0.601282:0.492635:0.591664:0.487008:0.591664:0.000000
(2):@0.488390:0.591656:0.500217:0.591656:0.500217:0.582038:0.488390:0.582038:0.000000:0.000000:0.000000
, :@0.500182:0.598006:0.507021:0.598006:0.507021:0.581508:0.500182:0.581508:0.000000:0.000000
L:@0.507580:0.598121:0.515421:0.598121:0.515421:0.581653:0.507580:0.581653:0.000000
h:@0.515370:0.601282:0.520997:0.601282:0.520997:0.591664:0.515370:0.591664:0.000000
(3):@0.516751:0.591656:0.528578:0.591656:0.528578:0.582038:0.516751:0.582038:0.000000:0.000000:0.000000
, …, que pasan :@0.528544:0.598006:0.635505:0.598006:0.635505:0.581508:0.528544:0.581508:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
por el punto   y por cada uno :@0.404245:0.615356:0.635501:0.615356:0.635501:0.598859:0.404245:0.598859:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
P:@0.501168:0.615472:0.509953:0.615472:0.509953:0.599003:0.501168:0.599003:0.000000
0:@0.509904:0.618633:0.514857:0.618633:0.514857:0.609015:0.509904:0.609015:0.000000
de los puntos  ,  ,  , …, res-:@0.404241:0.632707:0.631388:0.632707:0.631388:0.616210:0.404241:0.616210:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
P P P:@0.512107:0.632823:0.567201:0.632823:0.567201:0.616354:0.512107:0.616354:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.520848:0.635984:0.525801:0.635984:0.525801:0.626366:0.520848:0.626366:0.000000
3:@0.544000:0.635984:0.548953:0.635984:0.548953:0.626366:0.544000:0.626366:0.000000
4:@0.567150:0.635984:0.572103:0.635984:0.572103:0.626366:0.567150:0.626366:0.000000
pectivamente, y la recta tangen-:@0.404250:0.650058:0.631370:0.650058:0.631370:0.633560:0.404250:0.633560:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
te   a la gráfica de la función  .:@0.404250:0.667409:0.615340:0.667409:0.615340:0.650911:0.404250:0.650911:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
L:@0.422283:0.667524:0.430124:0.667524:0.430124:0.651056:0.422283:0.651056:0.000000
f:@0.608347:0.667524:0.612643:0.667524:0.612643:0.651056:0.608347:0.651056:0.000000
Para | | que tiende a 0, los puntos  ,  ,  ,  , … se aproximan cada :@0.404250:0.705667:0.895916:0.705673:0.895916:0.689176:0.404250:0.689169:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
h:@0.444322:0.705783:0.453724:0.705783:0.453724:0.689314:0.444322:0.689314:0.000000
P P P P:@0.653464:0.705783:0.725862:0.705789:0.725862:0.689320:0.653464:0.689314:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.662226:0.708951:0.667180:0.708951:0.667180:0.699333:0.662226:0.699333:0.000000
2:@0.683438:0.708951:0.688392:0.708951:0.688392:0.699333:0.683438:0.699333:0.000000
3:@0.704650:0.708951:0.709603:0.708951:0.709603:0.699333:0.704650:0.699333:0.000000
4:@0.725860:0.708951:0.730814:0.708951:0.730814:0.699333:0.725860:0.699333:0.000000
vez más a   = ( ,  ( )), y las pendientes de las rectas :@0.404229:0.723024:0.788743:0.723024:0.788743:0.706526:0.404229:0.706526:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
P:@0.479672:0.723140:0.488457:0.723140:0.488457:0.706671:0.479672:0.706671:0.000000
0:@0.488461:0.726302:0.493414:0.726302:0.493414:0.716684:0.488461:0.716684:0.000000
a f a:@0.520384:0.723140:0.556448:0.723140:0.556448:0.706671:0.520384:0.706671:0.000000:0.000000:0.000000:0.000000:0.000000
L:@0.789706:0.723140:0.797547:0.723140:0.797547:0.706671:0.789706:0.706671:0.000000
h:@0.797539:0.726302:0.803166:0.726302:0.803166:0.716684:0.797539:0.716684:0.000000
(1):@0.798954:0.716676:0.810848:0.716676:0.810848:0.707057:0.798954:0.707057:0.000000:0.000000:0.000000
, :@0.810847:0.723024:0.817744:0.723024:0.817744:0.706526:0.810847:0.706526:0.000000:0.000000
L:@0.818707:0.723140:0.826548:0.723140:0.826548:0.706671:0.818707:0.706671:0.000000
h:@0.826547:0.726302:0.832174:0.726302:0.832174:0.716684:0.826547:0.716684:0.000000
(2):@0.827963:0.716676:0.839857:0.716676:0.839857:0.707057:0.827963:0.707057:0.000000:0.000000:0.000000
, :@0.839855:0.723024:0.846752:0.723024:0.846752:0.706526:0.839855:0.706526:0.000000:0.000000
L:@0.847716:0.723140:0.855557:0.723140:0.855557:0.706671:0.847716:0.706671:0.000000
h:@0.855556:0.726302:0.861183:0.726302:0.861183:0.716684:0.855556:0.716684:0.000000
(3):@0.856971:0.716676:0.868865:0.716676:0.868865:0.707057:0.856971:0.707057:0.000000:0.000000:0.000000
, … :@0.868866:0.723024:0.895914:0.723024:0.895914:0.706526:0.868866:0.706526:0.000000:0.000000:0.000000:0.000000
se aproximan cada vez más a la pendiente   de la recta  . En tal caso :@0.404245:0.740375:0.895920:0.740375:0.895920:0.723877:0.404245:0.723877:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
m:@0.704938:0.740491:0.719733:0.740491:0.719733:0.724022:0.704938:0.724022:0.000000
L:@0.801187:0.740491:0.809028:0.740491:0.809028:0.724022:0.801187:0.724022:0.000000
se escribe:@0.404245:0.757726:0.472866:0.757726:0.472866:0.741228:0.404245:0.741228:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
m lím Q h:@0.491035:0.782320:0.578500:0.782320:0.578500:0.765852:0.491035:0.765852:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 = :@0.505831:0.782205:0.524923:0.782205:0.524923:0.765707:0.505831:0.765707:0.000000:0.000000:0.000000
  ( ) = :@0.547117:0.782205:0.603544:0.782205:0.603544:0.765707:0.547117:0.765707:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
lím:@0.603544:0.782320:0.625738:0.782320:0.625738:0.765852:0.603544:0.765852:0.000000:0.000000:0.000000
                            =            .:@0.625738:0.782205:0.804982:0.782205:0.804982:0.765707:0.625738:0.765707:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Así, :@0.404245:0.816906:0.433355:0.816906:0.433355:0.800408:0.404245:0.800408:0.000000:0.000000:0.000000:0.000000:0.000000
la pendiente de la recta tangente a la gráfica de la función :@0.433355:0.817369:0.879706:0.817369:0.879706:0.800423:0.433355:0.800423:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
polinomial   en el punto :@0.404245:0.841848:0.587757:0.841848:0.587757:0.824902:0.404245:0.824902:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.490477:0.842079:0.495582:0.842079:0.495582:0.824916:0.490477:0.824916:0.000000
x = a:@0.587034:0.842079:0.623388:0.842079:0.623388:0.824916:0.587034:0.824916:0.000000:0.000000:0.000000:0.000000:0.000000
 es :@0.623291:0.841848:0.645976:0.841848:0.645976:0.824902:0.623291:0.824902:0.000000:0.000000:0.000000:0.000000
        ( ). La ecuación cartesiana de la:@0.645254:0.841385:0.891809:0.841385:0.891809:0.824888:0.645254:0.824888:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.678486:0.841501:0.687464:0.841501:0.687464:0.825032:0.678486:0.825032:0.000000
recta tangente a la gráfica de la función   está definida como::@0.404245:0.865864:0.835201:0.865864:0.835201:0.849367:0.404245:0.849367:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.687499:0.865980:0.691795:0.865980:0.691795:0.849511:0.687499:0.849511:0.000000
( ,  )    , tal que   –  ( ) =            (  –  ).:@0.404245:0.890343:0.705144:0.890343:0.705144:0.873846:0.404245:0.873846:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.410006:0.890459:0.431486:0.890459:0.431486:0.873990:0.410006:0.873990:0.000000:0.000000:0.000000
:@0.441004:0.890126:0.457051:0.890126:0.457051:0.875479:0.441004:0.875479:0.000000
:@0.460797:0.889256:0.474102:0.889256:0.474102:0.876394:0.460797:0.876394:0.000000
2:@0.473918:0.883990:0.478871:0.883990:0.478871:0.874372:0.473918:0.874372:0.000000
y f a:@0.538942:0.890459:0.584639:0.890459:0.584639:0.873990:0.538942:0.873990:0.000000:0.000000:0.000000:0.000000:0.000000
x a:@0.661200:0.890459:0.696436:0.890459:0.696436:0.873990:0.661200:0.873990:0.000000:0.000000:0.000000
f a + h:@0.533943:0.451973:0.581740:0.451973:0.581740:0.435504:0.533943:0.435504:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(:@0.538239:0.451857:0.544192:0.451857:0.544192:0.435359:0.538239:0.435359:0.000000
) –  ( ):@0.581740:0.451857:0.631657:0.451857:0.631657:0.435359:0.581740:0.435359:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f a:@0.606477:0.451973:0.625704:0.451973:0.625704:0.435504:0.606477:0.435504:0.000000:0.000000:0.000000
h:@0.578099:0.468311:0.587501:0.468311:0.587501:0.451843:0.578099:0.451843:0.000000
f a + h:@0.648466:0.402871:0.696263:0.402871:0.696263:0.386403:0.648466:0.386403:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(:@0.652762:0.402756:0.658715:0.402756:0.658715:0.386258:0.652762:0.386258:0.000000
) –  ( ):@0.696263:0.402756:0.746179:0.402756:0.746179:0.386258:0.696263:0.386258:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f a:@0.721000:0.402871:0.740226:0.402871:0.740226:0.386403:0.721000:0.386403:0.000000:0.000000:0.000000
h:@0.692622:0.419210:0.702023:0.419210:0.702023:0.402741:0.692622:0.402741:0.000000
h:@0.524977:0.791000:0.531109:0.791000:0.531109:0.780260:0.524977:0.780260:0.000000
→:@0.531109:0.790318:0.541856:0.790318:0.541856:0.780307:0.531109:0.780307:0.000000
0:@0.541855:0.790925:0.547396:0.790925:0.547396:0.780165:0.541855:0.780165:0.000000
h:@0.602780:0.791000:0.608911:0.791000:0.608911:0.780260:0.602780:0.780260:0.000000
→:@0.608914:0.790318:0.619661:0.790318:0.619661:0.780307:0.608914:0.780307:0.000000
0:@0.619660:0.790925:0.625201:0.790925:0.625201:0.780165:0.619660:0.780165:0.000000
f a + h:@0.634866:0.774899:0.682664:0.774899:0.682664:0.758430:0.634866:0.758430:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(:@0.639163:0.774783:0.645116:0.774783:0.645116:0.758286:0.639163:0.758286:0.000000
) –  ( ):@0.682664:0.774783:0.732580:0.774783:0.732580:0.758286:0.682664:0.758286:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f a:@0.707400:0.774899:0.726627:0.774899:0.726627:0.758430:0.707400:0.758430:0.000000:0.000000:0.000000
h:@0.679022:0.791238:0.688424:0.791238:0.688424:0.774769:0.679022:0.774769:0.000000
df a:@0.762089:0.774899:0.790486:0.774899:0.790486:0.758430:0.762089:0.758430:0.000000:0.000000:0.000000:0.000000
( ):@0.775556:0.774783:0.796439:0.774783:0.796439:0.758286:0.775556:0.758286:0.000000:0.000000:0.000000
dx:@0.771009:0.791238:0.787500:0.791238:0.787500:0.774769:0.771009:0.774769:0.000000:0.000000
df a:@0.612889:0.882812:0.641286:0.882812:0.641286:0.866343:0.612889:0.866343:0.000000:0.000000:0.000000:0.000000
( ):@0.626355:0.882696:0.647239:0.882696:0.647239:0.866199:0.626355:0.866199:0.000000:0.000000:0.000000
dx:@0.621809:0.899151:0.638300:0.899151:0.638300:0.882682:0.621809:0.882682:0.000000:0.000000
df:@0.649923:0.834146:0.663390:0.834146:0.663390:0.817677:0.649923:0.817677:0.000000:0.000000
dx:@0.648402:0.850484:0.664893:0.850484:0.664893:0.834016:0.648402:0.834016:0.000000:0.000000
0:@0.701903:0.633524:0.708921:0.633524:0.708921:0.619896:0.701903:0.619896:0.000000
y:@0.698115:0.492892:0.704465:0.492892:0.704465:0.479287:0.698115:0.479287:0.000000
x:@0.879559:0.635866:0.885734:0.635866:0.885734:0.622261:0.879559:0.622261:0.000000
f a:@0.688474:0.608809:0.701849:0.608809:0.701849:0.597353:0.688474:0.597353:0.000000:0.000000:0.000000
( ):@0.691463:0.608729:0.705990:0.608729:0.705990:0.597252:0.691463:0.597252:0.000000:0.000000:0.000000
a+h:@0.851857:0.635353:0.872214:0.635353:0.872214:0.623897:0.851857:0.623897:0.000000:0.000000:0.000000
1:@0.872216:0.637550:0.875662:0.637550:0.875662:0.630859:0.872216:0.630859:0.000000
a+h:@0.795448:0.635351:0.815806:0.635351:0.815806:0.623894:0.795448:0.623894:0.000000:0.000000:0.000000
4:@0.815806:0.637550:0.819251:0.637550:0.819251:0.630859:0.815806:0.630859:0.000000
P:@0.738998:0.614966:0.745109:0.614966:0.745109:0.603510:0.738998:0.603510:0.000000
0:@0.745109:0.617165:0.748555:0.617165:0.748555:0.610475:0.745109:0.610475:0.000000
P:@0.868981:0.522199:0.875092:0.522199:0.875092:0.510742:0.868981:0.510742:0.000000
1:@0.875092:0.524398:0.878538:0.524398:0.878538:0.517707:0.875092:0.517707:0.000000
L:@0.880957:0.598092:0.886412:0.598092:0.886412:0.586635:0.880957:0.586635:0.000000
L:@0.877312:0.574927:0.882767:0.574927:0.882767:0.563471:0.877312:0.563471:0.000000
(3):@0.882770:0.570478:0.890451:0.570478:0.890451:0.563799:0.882770:0.563799:0.000000:0.000000:0.000000
h:@0.884395:0.577128:0.888310:0.577128:0.888310:0.570437:0.884395:0.570437:0.000000
L:@0.876588:0.561101:0.882043:0.561101:0.882043:0.549644:0.876588:0.549644:0.000000
(2):@0.882043:0.556648:0.889723:0.556648:0.889723:0.549969:0.882043:0.549969:0.000000:0.000000:0.000000
h:@0.883668:0.563298:0.887583:0.563298:0.887583:0.556607:0.883668:0.556607:0.000000
L:@0.876588:0.546785:0.882043:0.546785:0.882043:0.535329:0.876588:0.535329:0.000000
(1):@0.882043:0.542333:0.889723:0.542333:0.889723:0.535653:0.882043:0.535653:0.000000:0.000000:0.000000
h:@0.883668:0.548982:0.887583:0.548982:0.887583:0.542292:0.883668:0.542292:0.000000
L:@0.877401:0.502948:0.882856:0.502948:0.882856:0.491492:0.877401:0.491492:0.000000
h:@0.882856:0.505147:0.886770:0.505147:0.886770:0.498457:0.882856:0.498457:0.000000
P:@0.840264:0.570317:0.846375:0.570317:0.846375:0.558860:0.840264:0.558860:0.000000
2:@0.846375:0.572516:0.849821:0.572516:0.849821:0.565825:0.846375:0.565825:0.000000
P:@0.826018:0.585455:0.832129:0.585455:0.832129:0.573998:0.826018:0.573998:0.000000
3:@0.832129:0.587654:0.835575:0.587654:0.835575:0.580963:0.832129:0.580963:0.000000
P:@0.809649:0.596503:0.815760:0.596503:0.815760:0.585046:0.809649:0.585046:0.000000
4:@0.815760:0.598702:0.819206:0.598702:0.819206:0.592011:0.815760:0.592011:0.000000
f a+h:@0.670918:0.590295:0.698405:0.590295:0.698405:0.578839:0.670918:0.578839:0.000000:0.000000:0.000000:0.000000:0.000000
(:@0.673906:0.590215:0.678047:0.590215:0.678047:0.578738:0.673906:0.578738:0.000000
4:@0.698403:0.592495:0.701849:0.592495:0.701849:0.585804:0.698403:0.585804:0.000000
):@0.701849:0.590215:0.705990:0.590215:0.705990:0.578738:0.701849:0.578738:0.000000
f a+h:@0.670918:0.519353:0.698405:0.519353:0.698405:0.507897:0.670918:0.507897:0.000000:0.000000:0.000000:0.000000:0.000000
(:@0.673906:0.519273:0.678047:0.519273:0.678047:0.507796:0.673906:0.507796:0.000000
1:@0.698403:0.521551:0.701849:0.521551:0.701849:0.514861:0.698403:0.514861:0.000000
):@0.701849:0.519272:0.705990:0.519272:0.705990:0.507795:0.701849:0.507795:0.000000
p:@0.828839:0.676805:0.840320:0.676805:0.840320:0.666781:0.828839:0.666781:0.000000
 :@0.840320:0.677513:0.843201:0.677513:0.843201:0.666036:0.840320:0.666036:0.000000
Figura 4.1.:@0.843201:0.677513:0.891769:0.677513:0.891769:0.666036:0.843201:0.666036:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ministerio de Agricultura y Ganaderia Ecuador. www.flirck.com:@0.141334:0.747533:0.141334:0.573062:0.129865:0.573062:0.129865:0.747533:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Competencia :@0.199644:0.383034:0.297267:0.383034:0.297267:0.367561:0.199644:0.367561:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
socioemocional:@0.199644:0.395602:0.310020:0.395602:0.310020:0.380129:0.199644:0.380129:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
En ocasiones en la vida :@0.199880:0.420076:0.352175:0.420076:0.352175:0.405013:0.199880:0.405013:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
nos enfrentamos a problemas :@0.153337:0.435918:0.349621:0.435918:0.349621:0.420855:0.153337:0.420855:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
que requieren un mejor modo :@0.153337:0.451760:0.354530:0.451760:0.354530:0.436697:0.153337:0.436697:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de realizar las cosas. Por ejem-:@0.153337:0.467602:0.346368:0.467602:0.346368:0.452539:0.153337:0.452539:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
plo, un agricultor siempre trata :@0.153337:0.483444:0.357293:0.483444:0.357293:0.468381:0.153337:0.468381:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de escoger la mejor mezcla de :@0.153337:0.499286:0.352154:0.499286:0.352154:0.484223:0.153337:0.484223:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cultivos de tal manera que sea :@0.153337:0.515128:0.352894:0.515128:0.352894:0.500065:0.153337:0.500065:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la más apropiada para aprove-:@0.153337:0.530970:0.348813:0.530970:0.348813:0.515907:0.153337:0.515907:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
char el suelo. Algunas veces un :@0.153337:0.546812:0.355886:0.546812:0.355886:0.531749:0.153337:0.531749:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
problema de esta naturaleza :@0.153337:0.562654:0.340511:0.562654:0.340511:0.547591:0.153337:0.547591:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
implica el uso de la derivada :@0.153337:0.578496:0.340036:0.578496:0.340036:0.563433:0.153337:0.563433:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
para su solución.:@0.153337:0.594338:0.261340:0.594338:0.261340:0.579275:0.153337:0.579275:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Valoras el estudio de la mate-:@0.153344:0.773201:0.348980:0.773201:0.348980:0.758137:0.153344:0.758137:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
mática? :@0.153344:0.789042:0.206360:0.789042:0.206360:0.773979:0.153344:0.773979:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Justifica:@0.206360:0.789465:0.262242:0.789465:0.262242:0.773993:0.206360:0.773993:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 tu respuesta.:@0.262244:0.789042:0.348345:0.789042:0.348345:0.773979:0.262244:0.773979:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000