147:@0.918240:0.966765:0.943652:0.966765:0.943652:0.950778:0.918240:0.950778:0.000000:0.000000:0.000000
Competencia digital:@0.684804:0.381243:0.827156:0.381243:0.827156:0.365771:0.684804:0.365771:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Visita:@0.685042:0.410069:0.722667:0.410069:0.722667:0.394808:0.685042:0.394808:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 esta página para :@0.722667:0.409871:0.835294:0.409871:0.835294:0.394808:0.722667:0.394808:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
conocer más sobre el cálculo de :@0.638498:0.425713:0.849717:0.425713:0.849717:0.410650:0.638498:0.410650:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
funciones derivadas: :@0.638498:0.441555:0.773430:0.441555:0.773430:0.426492:0.638498:0.426492:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
lynk.ec/12m08:@0.638498:0.464856:0.736387:0.464856:0.736387:0.449542:0.638498:0.449542:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Derivada de la función cuadrática :@0.108233:0.108020:0.382671:0.108020:0.382671:0.090337:0.108233:0.090337:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sean  ,  ,       con   ≠ 0. La función cuadrática está definida como: :@0.108233:0.124727:0.599898:0.124727:0.599898:0.108230:0.108233:0.108230:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a b c:@0.145723:0.124843:0.184331:0.124843:0.184331:0.108374:0.145723:0.108374:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.188550:0.124511:0.204598:0.124511:0.204598:0.109864:0.188550:0.109864:0.000000
:@0.209202:0.123759:0.223112:0.123759:0.223112:0.110312:0.209202:0.110312:0.000000
a:@0.257731:0.124843:0.266709:0.124843:0.266709:0.108374:0.257731:0.108374:0.000000
f x:@0.256633:0.149322:0.274357:0.149322:0.274357:0.132853:0.256633:0.132853:0.000000:0.000000:0.000000
( ) = :@0.260929:0.149206:0.299402:0.149206:0.299402:0.132709:0.260929:0.132709:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ax:@0.299402:0.149322:0.315874:0.149322:0.315874:0.132853:0.299402:0.132853:0.000000:0.000000
2:@0.315877:0.142854:0.320831:0.142854:0.320831:0.133236:0.315877:0.133236:0.000000
 +   +  ,        .:@0.320831:0.149207:0.447365:0.149207:0.447365:0.132709:0.320831:0.132709:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
bx c x:@0.339923:0.149323:0.405598:0.149323:0.405598:0.132854:0.339923:0.132854:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.409740:0.148990:0.425788:0.148990:0.425788:0.134343:0.409740:0.134343:0.000000
:@0.430701:0.148238:0.444610:0.148238:0.444610:0.134791:0.430701:0.134791:0.000000
Calculemos         ( ) o  ( ). Para el efecto, estudiemos el límite del :@0.108239:0.183909:0.573166:0.183909:0.573166:0.167411:0.108239:0.167411:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.234347:0.184024:0.241822:0.184024:0.241822:0.167555:0.234347:0.167555:0.000000
f' x:@0.265596:0.184024:0.287078:0.184024:0.287078:0.167555:0.265596:0.167555:0.000000:0.000000:0.000000:0.000000
cociente incremental. Para x     y   ≠ 0, de la definición de la fun-:@0.108239:0.208388:0.595841:0.208388:0.595841:0.191890:0.108239:0.191890:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.313973:0.208171:0.330021:0.208171:0.330021:0.193524:0.313973:0.193524:0.000000
:@0.335492:0.207419:0.349401:0.207419:0.349401:0.193972:0.335492:0.193972:0.000000
h:@0.366663:0.208503:0.376065:0.208503:0.376065:0.192034:0.366663:0.192034:0.000000
ción  , se tiene: :@0.108258:0.225738:0.215660:0.225738:0.215660:0.209241:0.108258:0.209241:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.143302:0.225854:0.147598:0.225854:0.147598:0.209385:0.143302:0.209385:0.000000
f x h:@0.108258:0.250333:0.154476:0.250333:0.154476:0.233864:0.108258:0.233864:0.000000:0.000000:0.000000:0.000000:0.000000
(  +  ) =  (  +  )  +  (  +  ) + :@0.112554:0.250217:0.336622:0.250216:0.336622:0.233718:0.112554:0.233720:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a x h:@0.179520:0.250333:0.230419:0.250333:0.230419:0.233864:0.179520:0.233864:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.236344:0.243864:0.241297:0.243864:0.241297:0.234246:0.236344:0.234246:0.000000
b x h:@0.260389:0.250332:0.311577:0.250332:0.311577:0.233863:0.260389:0.233863:0.000000:0.000000:0.000000:0.000000:0.000000
c:@0.336622:0.250332:0.343808:0.250332:0.343808:0.233863:0.336622:0.233863:0.000000
 :@0.108232:0.267683:0.112374:0.267683:0.112374:0.251214:0.108232:0.251214:0.000000
= a x:@0.165200:0.267683:0.202632:0.267683:0.202632:0.251214:0.165200:0.251214:0.000000:0.000000:0.000000:0.000000:0.000000
(  + 2  +  ) +  (  +  ) + :@0.189204:0.267567:0.386724:0.267567:0.386724:0.251069:0.189204:0.251069:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.202623:0.261215:0.207576:0.261215:0.207576:0.251597:0.202623:0.251597:0.000000
xh h:@0.235164:0.267683:0.280495:0.267683:0.280495:0.251214:0.235164:0.251214:0.000000:0.000000:0.000000:0.000000
2:@0.280493:0.261215:0.285446:0.261215:0.285446:0.251597:0.280493:0.251597:0.000000
b x h:@0.310491:0.267683:0.361679:0.267683:0.361679:0.251214:0.310491:0.251214:0.000000:0.000000:0.000000:0.000000:0.000000
c:@0.386724:0.267683:0.393910:0.267683:0.393910:0.251214:0.386724:0.251214:0.000000
 :@0.108225:0.285033:0.112367:0.285033:0.112367:0.268565:0.108225:0.268565:0.000000
= ax:@0.165193:0.285033:0.196692:0.285033:0.196692:0.268565:0.165193:0.268565:0.000000:0.000000:0.000000:0.000000
2:@0.196689:0.278566:0.201642:0.278566:0.201642:0.268948:0.196689:0.268948:0.000000
 + 2:@0.201643:0.284918:0.229231:0.284918:0.229231:0.268420:0.201643:0.268420:0.000000:0.000000:0.000000:0.000000
axh ah:@0.229231:0.285033:0.292421:0.285033:0.292421:0.268565:0.229231:0.268565:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 + :@0.255065:0.284918:0.274157:0.284918:0.274157:0.268420:0.255065:0.268420:0.000000:0.000000:0.000000
2:@0.292417:0.278566:0.297370:0.278566:0.297370:0.268948:0.292417:0.268948:0.000000
 +   +   + :@0.297371:0.284918:0.389979:0.284918:0.389979:0.268420:0.297371:0.268420:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
bx bh c:@0.316463:0.285033:0.397165:0.285033:0.397165:0.268565:0.316463:0.268565:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.108244:0.302384:0.112386:0.302384:0.112386:0.285915:0.108244:0.285915:0.000000
= ax:@0.165211:0.302384:0.196710:0.302384:0.196710:0.285915:0.165211:0.285915:0.000000:0.000000:0.000000:0.000000
2:@0.196689:0.295917:0.201642:0.295917:0.201642:0.286298:0.196689:0.286298:0.000000
 +   +   +  (2:@0.201643:0.302268:0.306696:0.302268:0.306696:0.285771:0.201643:0.285771:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
bx c h ax  b ah:@0.220735:0.302384:0.388882:0.302384:0.388882:0.285915:0.220735:0.285915:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
+   +  ):@0.327310:0.302268:0.394835:0.302268:0.394835:0.285771:0.327310:0.285771:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.108244:0.319735:0.112386:0.319735:0.112386:0.303266:0.108244:0.303266:0.000000
= f x   h ax  b ah:@0.165211:0.319735:0.329043:0.319735:0.329043:0.303266:0.165211:0.303266:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( ) +  (2:@0.184534:0.319619:0.246857:0.319619:0.246857:0.303121:0.184534:0.303121:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
+   +  ).:@0.267471:0.319619:0.337751:0.319619:0.337751:0.303121:0.267471:0.303121:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Luego, :@0.108263:0.356793:0.158372:0.356793:0.158372:0.340295:0.108263:0.340295:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x h:@0.160888:0.351255:0.207105:0.351255:0.207105:0.334787:0.160888:0.334787:0.000000:0.000000:0.000000:0.000000:0.000000
(  +  ) –  ( ):@0.165184:0.351140:0.255518:0.351140:0.255518:0.334642:0.165184:0.334642:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.231841:0.351255:0.249565:0.351255:0.249565:0.334787:0.231841:0.334787:0.000000:0.000000:0.000000
h:@0.203502:0.367594:0.212904:0.367594:0.212904:0.351125:0.203502:0.351125:0.000000
 = :@0.258061:0.356909:0.277230:0.356909:0.277230:0.340440:0.258061:0.340440:0.000000:0.000000:0.000000
h ax b ah:@0.278225:0.351255:0.384261:0.351255:0.384261:0.334787:0.278225:0.334787:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(2  +   +  ):@0.287626:0.351140:0.390214:0.351140:0.390214:0.334642:0.287626:0.334642:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
h :@0.329528:0.367594:0.343072:0.367594:0.343072:0.351125:0.329528:0.351125:0.000000:0.000000
 =  ax  b ah.:@0.391215:0.356909:0.503609:0.356909:0.503609:0.340440:0.391215:0.340440:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.410384:0.356793:0.418880:0.356793:0.418880:0.340295:0.410384:0.340295:0.000000
+   + :@0.439494:0.356793:0.482802:0.356793:0.482802:0.340295:0.439494:0.340295:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.347869:0.374144:0.352011:0.374144:0.352011:0.357646:0.347869:0.357646:0.000000
Como   es constante, es claro que para | | suficientemente pequeño,   :@0.108247:0.391495:0.599887:0.391495:0.599887:0.374997:0.108247:0.374997:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.157104:0.391610:0.166082:0.391610:0.166082:0.375142:0.157104:0.375142:0.000000
h:@0.392697:0.391610:0.402098:0.391610:0.402098:0.375142:0.392697:0.375142:0.000000
ah:@0.108247:0.408961:0.126511:0.408961:0.126511:0.392492:0.108247:0.392492:0.000000:0.000000
 también lo es. Entonces,:@0.126511:0.408845:0.301917:0.408845:0.301917:0.392348:0.126511:0.392348:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.108247:0.426196:0.112389:0.426196:0.112389:0.409698:0.108247:0.409698:0.000000
lím:@0.168837:0.445051:0.191030:0.445051:0.191030:0.428582:0.168837:0.428582:0.000000:0.000000:0.000000
 :@0.191030:0.444935:0.195172:0.444935:0.195172:0.428437:0.191030:0.428437:0.000000
f x h:@0.197714:0.440481:0.243932:0.440481:0.243932:0.424012:0.197714:0.424012:0.000000:0.000000:0.000000:0.000000:0.000000
(  +  ) –  ( ):@0.202010:0.440365:0.292345:0.440365:0.292345:0.423868:0.202010:0.423868:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.268668:0.440481:0.286392:0.440481:0.286392:0.424012:0.268668:0.424012:0.000000:0.000000:0.000000
h:@0.240329:0.456820:0.249730:0.456820:0.249730:0.440351:0.240329:0.440351:0.000000
 = :@0.294888:0.444934:0.313980:0.444934:0.313980:0.428437:0.294888:0.428437:0.000000:0.000000:0.000000
lím:@0.313980:0.445050:0.336174:0.445050:0.336174:0.428581:0.313980:0.428581:0.000000:0.000000:0.000000
 :@0.337137:0.444934:0.341279:0.444934:0.341279:0.428437:0.337137:0.428437:0.000000
h ax b ah:@0.344646:0.440856:0.450682:0.440856:0.450682:0.424387:0.344646:0.424387:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(2  +   +  ):@0.354048:0.440740:0.456635:0.440740:0.456635:0.424242:0.354048:0.424242:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
h:@0.395950:0.457194:0.405351:0.457194:0.405351:0.440725:0.395950:0.440725:0.000000
 = 2  +  ,:@0.460007:0.444933:0.535180:0.444933:0.535180:0.428435:0.460007:0.428435:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ax b:@0.487594:0.445049:0.532425:0.445049:0.532425:0.428580:0.487594:0.428580:0.000000:0.000000:0.000000:0.000000
Así, la derivada de la función cuadrática es::@0.108242:0.480733:0.410568:0.480733:0.410568:0.464236:0.108242:0.464236:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
        ( ) = :@0.108242:0.505704:0.183280:0.505704:0.183280:0.489206:0.108242:0.489206:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f' x:@0.137236:0.505820:0.158236:0.505820:0.158236:0.489351:0.137236:0.489351:0.000000:0.000000:0.000000:0.000000
lím :@0.183280:0.505820:0.209616:0.505820:0.209616:0.489351:0.183280:0.489351:0.000000:0.000000:0.000000:0.000000
f x h:@0.212152:0.502148:0.258369:0.502148:0.258369:0.485679:0.212152:0.485679:0.000000:0.000000:0.000000:0.000000:0.000000
(  +  ) –  ( ):@0.216448:0.502032:0.306782:0.502032:0.306782:0.485534:0.216448:0.485534:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.283105:0.502148:0.300829:0.502148:0.300829:0.485679:0.283105:0.485679:0.000000:0.000000:0.000000
h:@0.254766:0.518486:0.264168:0.518486:0.264168:0.502018:0.254766:0.502018:0.000000
 = 2  + :@0.309325:0.505705:0.372477:0.505705:0.372477:0.489207:0.309325:0.489207:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ax b.:@0.336913:0.505820:0.384171:0.505820:0.384171:0.489352:0.336913:0.489352:0.000000:0.000000:0.000000:0.000000:0.000000
Conclusión:  ( ) = :@0.108235:0.541505:0.237447:0.541505:0.237447:0.525007:0.108235:0.525007:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.195275:0.541621:0.212999:0.541621:0.212999:0.525152:0.195275:0.525152:0.000000:0.000000:0.000000
ax:@0.236850:0.541621:0.253321:0.541621:0.253321:0.525152:0.236850:0.525152:0.000000:0.000000
2:@0.253326:0.535153:0.258279:0.535153:0.258279:0.525535:0.253326:0.525535:0.000000
 +   +  ,        , la derivada es:   ( ) = 2  + :@0.258279:0.541505:0.584666:0.541505:0.584666:0.525007:0.258279:0.525007:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
bx c:@0.276177:0.541621:0.318002:0.541621:0.318002:0.525152:0.276177:0.525152:0.000000:0.000000:0.000000:0.000000
∀:@0.331408:0.549092:0.342981:0.549092:0.342981:0.530092:0.331408:0.530092:0.000000
x:@0.342989:0.541621:0.350464:0.541621:0.350464:0.525152:0.342989:0.525152:0.000000
:@0.354011:0.540986:0.368663:0.540986:0.368663:0.527613:0.354011:0.527613:0.000000
:@0.372209:0.540536:0.386118:0.540536:0.386118:0.527089:0.372209:0.527089:0.000000
f' x:@0.496333:0.541621:0.517353:0.541621:0.517353:0.525152:0.496333:0.525152:0.000000:0.000000:0.000000:0.000000
ax b.:@0.549700:0.541621:0.595763:0.541621:0.595763:0.525152:0.549700:0.525152:0.000000:0.000000:0.000000:0.000000:0.000000
Ejercicios resueltos:@0.108236:0.570553:0.238892:0.570553:0.238892:0.553766:0.108236:0.553766:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1.:@0.108236:0.597808:0.120508:0.597808:0.120508:0.581094:0.108236:0.581094:0.000000:0.000000
  Para  ( ) =  ,       ,   :@0.120508:0.597592:0.297306:0.597581:0.297306:0.581083:0.120508:0.581094:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.165319:0.597708:0.182658:0.597708:0.182658:0.581239:0.165319:0.581239:0.000000:0.000000:0.000000
x:@0.206393:0.597708:0.213868:0.597708:0.213868:0.581239:0.206393:0.581239:0.000000
2:@0.213676:0.591229:0.218629:0.591229:0.218629:0.581611:0.213676:0.581611:0.000000
∀:@0.228628:0.605167:0.240200:0.605167:0.240200:0.586168:0.228628:0.586168:0.000000
x:@0.240024:0.597696:0.247499:0.597696:0.247499:0.581228:0.240024:0.581228:0.000000
:@0.251081:0.597062:0.265733:0.597062:0.265733:0.583689:0.251081:0.583689:0.000000
:@0.269332:0.596612:0.283242:0.596612:0.283242:0.583165:0.269332:0.583165:0.000000
       x:@0.296940:0.597696:0.332811:0.597696:0.332811:0.581228:0.296940:0.581228:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( ) = 2  Para   = –1, se tiene  (–1) = –2.:@0.319596:0.597581:0.595782:0.597581:0.595782:0.581083:0.319596:0.581083:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x.:@0.364850:0.597696:0.375099:0.597696:0.375099:0.581228:0.364850:0.581228:0.000000:0.000000
x:@0.412030:0.597696:0.419505:0.597696:0.419505:0.581228:0.412030:0.581228:0.000000
f':@0.518760:0.597696:0.526312:0.597696:0.526312:0.581228:0.518760:0.581228:0.000000:0.000000
2.:@0.108236:0.632499:0.120508:0.632499:0.120508:0.615785:0.108236:0.615785:0.000000:0.000000
  Para  ( ) = 10  – 3  + 1,       ,   :@0.120508:0.632282:0.383111:0.632282:0.383111:0.615785:0.120508:0.615785:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.166456:0.632398:0.184180:0.632398:0.184180:0.615929:0.166456:0.615929:0.000000:0.000000:0.000000
x:@0.226217:0.632398:0.233692:0.632398:0.233692:0.615929:0.226217:0.615929:0.000000
2:@0.233695:0.625930:0.238648:0.625930:0.238648:0.616312:0.233695:0.616312:0.000000
x:@0.265928:0.632398:0.273403:0.632398:0.273403:0.615929:0.265928:0.615929:0.000000
∀:@0.312028:0.639869:0.323600:0.639869:0.323600:0.620870:0.312028:0.620870:0.000000
x:@0.323609:0.632398:0.331083:0.632398:0.331083:0.615929:0.323609:0.615929:0.000000
:@0.335225:0.631764:0.349877:0.631764:0.349877:0.618390:0.335225:0.618390:0.000000
:@0.354020:0.631313:0.367930:0.631313:0.367930:0.617867:0.354020:0.617867:0.000000
       x:@0.383111:0.632398:0.421391:0.632398:0.421391:0.615929:0.383111:0.615929:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( ) = 20:@0.407963:0.632282:0.463427:0.632282:0.463427:0.615785:0.407963:0.615785:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x –  .:@0.463427:0.632398:0.500571:0.632398:0.500571:0.615929:0.463427:0.615929:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3:@0.489224:0.632282:0.497720:0.632282:0.497720:0.615785:0.489224:0.615785:0.000000
Para  = 0,4,   :@0.131968:0.656762:0.226984:0.656762:0.226984:0.640264:0.131968:0.640264:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.166453:0.656878:0.173928:0.656878:0.173928:0.640409:0.166453:0.640409:0.000000
      :@0.226984:0.656878:0.251836:0.656878:0.251836:0.640409:0.226984:0.640409:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(0,4) = 5.:@0.251836:0.656762:0.313832:0.656762:0.313832:0.640264:0.251836:0.640264:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3.:@0.108233:0.691680:0.120505:0.691680:0.120505:0.674966:0.108233:0.674966:0.000000:0.000000
  ( ) = –7  + 9,       ,   :@0.120506:0.691463:0.315875:0.691462:0.315875:0.674964:0.120506:0.674966:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.131968:0.691579:0.149692:0.691579:0.149692:0.675110:0.131968:0.675110:0.000000:0.000000:0.000000
x:@0.193732:0.691579:0.201207:0.691579:0.201207:0.675110:0.193732:0.675110:0.000000
2:@0.201214:0.685110:0.206167:0.685110:0.206167:0.675492:0.201214:0.675492:0.000000
∀:@0.244794:0.699049:0.256366:0.699049:0.256366:0.680049:0.244794:0.680049:0.000000
x:@0.256374:0.691578:0.263849:0.691578:0.263849:0.675109:0.256374:0.675109:0.000000
:@0.267991:0.690943:0.282643:0.690943:0.282643:0.677570:0.267991:0.677570:0.000000
:@0.286784:0.690493:0.300694:0.690493:0.300694:0.677047:0.286784:0.677047:0.000000
       x:@0.315875:0.691578:0.354155:0.691578:0.354155:0.675109:0.315875:0.675109:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( ) =  14 ,        (0) = 0.:@0.340727:0.691462:0.500340:0.691462:0.500340:0.674964:0.340727:0.674964:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
– x:@0.379200:0.691578:0.413704:0.691578:0.413704:0.675109:0.379200:0.675109:0.000000:0.000000:0.000000
4.:@0.108234:0.726381:0.120506:0.726381:0.120506:0.709666:0.108234:0.709666:0.000000:0.000000
  ( ) = –       + 0,1 ,  :@0.120506:0.726164:0.275734:0.726164:0.275734:0.709666:0.120506:0.709666:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.131970:0.726279:0.149694:0.726279:0.149694:0.709811:0.131970:0.709811:0.000000:0.000000:0.000000
x:@0.205948:0.726279:0.213423:0.726279:0.213423:0.709811:0.205948:0.709811:0.000000
2:@0.213428:0.719812:0.218381:0.719812:0.218381:0.710194:0.213428:0.710194:0.000000
x:@0.257220:0.726279:0.264695:0.726279:0.264695:0.709811:0.257220:0.709811:0.000000
       :@0.275732:0.725249:0.306514:0.725249:0.306514:0.712192:0.275732:0.712192:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( ) =  5 + 0,1,                   = 0.:@0.306514:0.726164:0.517488:0.726164:0.517488:0.709666:0.306514:0.709666:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.312467:0.726279:0.319942:0.726279:0.319942:0.709811:0.312467:0.709811:0.000000
– x :@0.344987:0.726279:0.375137:0.726279:0.375137:0.709811:0.344987:0.709811:0.000000:0.000000:0.000000:0.000000
df:@0.206075:0.177025:0.219542:0.177025:0.219542:0.160556:0.206075:0.160556:0.000000:0.000000
dx:@0.204553:0.193363:0.221045:0.193363:0.221045:0.176895:0.204553:0.176895:0.000000:0.000000
h:@0.168275:0.452098:0.174407:0.452098:0.174407:0.441358:0.168275:0.441358:0.000000
→:@0.174407:0.451416:0.185154:0.451416:0.185154:0.441405:0.174407:0.441405:0.000000
0:@0.185153:0.452023:0.190694:0.452023:0.190694:0.441264:0.185153:0.441264:0.000000
h:@0.183796:0.512213:0.189928:0.512213:0.189928:0.501473:0.183796:0.501473:0.000000
→:@0.189926:0.511528:0.200674:0.511528:0.200674:0.501517:0.189926:0.501517:0.000000
0:@0.200673:0.512135:0.206214:0.512135:0.206214:0.501375:0.200673:0.501375:0.000000
h:@0.312621:0.452095:0.318752:0.452095:0.318752:0.441355:0.312621:0.441355:0.000000
→:@0.318755:0.451416:0.329503:0.451416:0.329503:0.441405:0.318755:0.441405:0.000000
0:@0.329500:0.452023:0.335041:0.452023:0.335041:0.441264:0.329500:0.441264:0.000000
df:@0.299757:0.590023:0.313223:0.590023:0.313223:0.573554:0.299757:0.573554:0.000000:0.000000
dx:@0.298235:0.606362:0.314726:0.606362:0.314726:0.589893:0.298235:0.589893:0.000000:0.000000
df:@0.382899:0.624205:0.396365:0.624205:0.396365:0.607737:0.382899:0.607737:0.000000:0.000000
dx:@0.381377:0.640544:0.397868:0.640544:0.397868:0.624075:0.381377:0.624075:0.000000:0.000000
df:@0.315098:0.683410:0.328565:0.683410:0.328565:0.666942:0.315098:0.666942:0.000000:0.000000
dx:@0.313576:0.699749:0.330067:0.699749:0.330067:0.683280:0.313576:0.683280:0.000000:0.000000
df:@0.426745:0.683410:0.440211:0.683410:0.440211:0.666942:0.426745:0.666942:0.000000:0.000000
dx:@0.425223:0.699749:0.441714:0.699749:0.441714:0.683280:0.425223:0.683280:0.000000:0.000000
df:@0.283585:0.718158:0.297052:0.718158:0.297052:0.701690:0.283585:0.701690:0.000000:0.000000
dx:@0.282063:0.734497:0.298555:0.734497:0.298555:0.718028:0.282063:0.718028:0.000000:0.000000
df:@0.427035:0.718158:0.440501:0.718158:0.440501:0.701690:0.427035:0.701690:0.000000:0.000000
dx:@0.425513:0.734497:0.442004:0.734497:0.442004:0.718028:0.425513:0.718028:0.000000:0.000000
df:@0.229884:0.648671:0.243350:0.648671:0.243350:0.632202:0.229884:0.632202:0.000000:0.000000
dx:@0.228362:0.665010:0.244853:0.665010:0.244853:0.648541:0.228362:0.648541:0.000000:0.000000
5:@0.192638:0.718043:0.201134:0.718043:0.201134:0.701545:0.192638:0.701545:0.000000
2:@0.192638:0.734381:0.201134:0.734381:0.201134:0.717884:0.192638:0.717884:0.000000
1:@0.462709:0.718043:0.471205:0.718043:0.471205:0.701545:0.462709:0.701545:0.000000
50:@0.458470:0.734381:0.475462:0.734381:0.475462:0.717884:0.458470:0.717884:0.000000:0.000000
Competencia :@0.684408:0.718244:0.782031:0.718244:0.782031:0.702772:0.684408:0.702772:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemática:@0.684408:0.730812:0.768471:0.730812:0.768471:0.715340:0.684408:0.715340:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sean  ,      . La distan-:@0.684646:0.755286:0.841269:0.755286:0.841269:0.740223:0.684646:0.740223:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.718982:0.755392:0.739052:0.755392:0.739052:0.740355:0.718982:0.740355:0.000000:0.000000:0.000000
:@0.742797:0.754787:0.756054:0.754787:0.756054:0.742687:0.742797:0.742687:0.000000
:@0.759836:0.754284:0.771931:0.754284:0.771931:0.742591:0.759836:0.742591:0.000000
cia de   a   se denota  ( ,  ), y :@0.638106:0.771128:0.836168:0.771128:0.836168:0.756065:0.638106:0.756065:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.679724:0.771234:0.708291:0.771234:0.708291:0.756197:0.679724:0.756197:0.000000:0.000000:0.000000
d x y:@0.779563:0.771234:0.813512:0.771234:0.813512:0.756197:0.779563:0.756197:0.000000:0.000000:0.000000:0.000000:0.000000
se lee “distancia de   a  \.:@0.638106:0.786970:0.798490:0.786970:0.798490:0.771907:0.638106:0.771907:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.762923:0.787076:0.791490:0.787076:0.791490:0.772039:0.762923:0.772039:0.000000:0.000000:0.000000
El conjunto de todas las fun-:@0.638106:0.809941:0.823853:0.809941:0.823853:0.794878:0.638106:0.794878:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ciones polinomiales de grado :@0.638106:0.825783:0.831841:0.825783:0.831841:0.810720:0.638106:0.810720:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
≤ 4 con coeficientes reales se :@0.638106:0.841625:0.829236:0.841625:0.829236:0.826562:0.638106:0.826562:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
denota con  [ ].:@0.638106:0.857467:0.754757:0.857466:0.754757:0.842403:0.638106:0.842404:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
P:@0.716908:0.857573:0.724929:0.857573:0.724929:0.842536:0.716908:0.842536:0.000000
4:@0.724931:0.860458:0.729453:0.860458:0.729453:0.851676:0.724931:0.851676:0.000000
:@0.734801:0.856463:0.746896:0.856463:0.746896:0.844770:0.734801:0.844770:0.000000
El cociente incremental de la :@0.638100:0.880437:0.828071:0.880437:0.828071:0.865374:0.638100:0.865374:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
función polinomial   en el pun-:@0.638100:0.896279:0.843902:0.896279:0.843902:0.881216:0.638100:0.881216:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.765908:0.896385:0.774368:0.896385:0.774368:0.881348:0.765908:0.881348:0.000000
to   se denota  ( ). Cuando :@0.638100:0.912121:0.827985:0.912121:0.827985:0.897058:0.638100:0.897058:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.656060:0.912227:0.664257:0.912227:0.664257:0.897190:0.656060:0.897190:0.000000
Q h:@0.735532:0.912227:0.760404:0.912227:0.760404:0.897190:0.735532:0.897190:0.000000:0.000000:0.000000
p:@0.638100:0.928069:0.646561:0.928069:0.646561:0.913032:0.638100:0.913032:0.000000
    [ ],       fijo,      , tal :@0.646561:0.927963:0.848516:0.927962:0.848516:0.912899:0.646561:0.912900:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.650351:0.927462:0.663608:0.927462:0.663608:0.915362:0.650351:0.915362:0.000000
P:@0.667389:0.928067:0.675410:0.928067:0.675410:0.913031:0.667389:0.913031:0.000000
4:@0.675411:0.930954:0.679933:0.930954:0.679933:0.922172:0.675411:0.922172:0.000000
:@0.685279:0.926959:0.697375:0.926959:0.697375:0.915266:0.685279:0.915266:0.000000
a:@0.709019:0.928067:0.717216:0.928067:0.717216:0.913031:0.709019:0.913031:0.000000
:@0.720997:0.927462:0.734254:0.927462:0.734254:0.915362:0.720997:0.915362:0.000000
:@0.738036:0.926959:0.750131:0.926959:0.750131:0.915266:0.738036:0.915266:0.000000
h:@0.780509:0.928067:0.789093:0.928067:0.789093:0.913031:0.780509:0.913031:0.000000
:@0.792873:0.927462:0.806130:0.927462:0.806130:0.915362:0.792873:0.915362:0.000000
:@0.809912:0.926959:0.822007:0.926959:0.822007:0.915266:0.809912:0.915266:0.000000
que   ≠ 0.:@0.638104:0.943804:0.702835:0.943804:0.702835:0.928741:0.638104:0.928741:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
h:@0.666547:0.943909:0.675131:0.943909:0.675131:0.928873:0.666547:0.928873:0.000000
Competencia :@0.685072:0.103570:0.782695:0.103570:0.782695:0.088097:0.685072:0.088097:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemática:@0.685072:0.116138:0.769134:0.116138:0.769134:0.100665:0.685072:0.100665:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
De la función polinomial :@0.685308:0.140612:0.849282:0.140612:0.849282:0.125549:0.685308:0.125549:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tenemos, entre otros, estos tres :@0.638765:0.156454:0.842366:0.156454:0.842366:0.141391:0.638765:0.141391:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tipos::@0.638765:0.172296:0.673890:0.172296:0.673890:0.157233:0.638765:0.157233:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Lineal:@0.638765:0.195689:0.680293:0.195689:0.680293:0.180217:0.638765:0.180217:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
, definida por:@0.680258:0.195267:0.765990:0.195267:0.765990:0.180204:0.680258:0.180204:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.638765:0.211215:0.654877:0.211215:0.654877:0.196178:0.638765:0.196178:0.000000:0.000000:0.000000
( ) = :@0.642652:0.211109:0.677603:0.211109:0.677603:0.196046:0.642652:0.196046:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
mx b x:@0.677568:0.211215:0.736653:0.211215:0.736653:0.196178:0.677568:0.196178:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 +  ,      .:@0.697850:0.211109:0.772692:0.211108:0.772692:0.196045:0.697850:0.196046:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.740438:0.210608:0.753695:0.210608:0.753695:0.198508:0.740438:0.198508:0.000000
:@0.757476:0.210223:0.770176:0.210223:0.770176:0.197946:0.757476:0.197946:0.000000
Cuadrática:@0.638779:0.234501:0.715718:0.234501:0.715718:0.219029:0.638779:0.219029:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
, definida por:@0.715683:0.234079:0.801416:0.234079:0.801416:0.219016:0.715683:0.219016:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.638779:0.250026:0.654891:0.250026:0.654891:0.234990:0.638779:0.234990:0.000000:0.000000:0.000000
( ) = :@0.642666:0.249921:0.677618:0.249921:0.677618:0.234858:0.642666:0.234858:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ax:@0.677583:0.250026:0.692587:0.250026:0.692587:0.234990:0.677583:0.234990:0.000000:0.000000
2:@0.692542:0.244120:0.697064:0.244120:0.697064:0.235338:0.692542:0.235338:0.000000
 +   +  ,      .:@0.697043:0.249919:0.802558:0.249919:0.802558:0.234856:0.697043:0.234856:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
bx c x:@0.714369:0.250025:0.766524:0.250025:0.766524:0.234988:0.714369:0.234988:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.770305:0.249420:0.783562:0.249420:0.783562:0.237320:0.770305:0.237320:0.000000
:@0.787343:0.249035:0.800043:0.249035:0.800043:0.236757:0.787343:0.236757:0.000000
Cúbica:@0.638777:0.273313:0.687166:0.273313:0.687166:0.257840:0.638777:0.257840:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
, definida por:@0.687132:0.272890:0.772866:0.272890:0.772866:0.257827:0.687132:0.257827:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.638777:0.288838:0.654890:0.288838:0.654890:0.273801:0.638777:0.273801:0.000000:0.000000:0.000000
( ) =   +   +  ,       .:@0.642665:0.288732:0.798125:0.288732:0.798125:0.273669:0.642665:0.273669:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.677581:0.288838:0.684406:0.288838:0.684406:0.273801:0.677581:0.273801:0.000000
3:@0.684363:0.282932:0.688886:0.282932:0.688886:0.274150:0.684363:0.274150:0.000000
bx c x:@0.706191:0.288838:0.762092:0.288838:0.762092:0.273801:0.706191:0.273801:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.765872:0.288232:0.779129:0.288232:0.779129:0.276133:0.765872:0.276133:0.000000
:@0.782910:0.287848:0.795610:0.287848:0.795610:0.275570:0.782910:0.275570:0.000000
Competencia :@0.163250:0.755347:0.260873:0.755347:0.260873:0.739874:0.163250:0.739874:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemática:@0.163250:0.767915:0.247312:0.767915:0.247312:0.752442:0.163250:0.752442:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
De la primera derivada obtenemos los intervalos de crecimiento y :@0.163487:0.792388:0.589799:0.792388:0.589799:0.777325:0.163487:0.777325:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
decrecimiento de la función y los posibles máximos y mínimos relativos. :@0.116944:0.808230:0.583799:0.808230:0.583799:0.793167:0.116944:0.793167:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
El límite:@0.116944:0.831201:0.168184:0.831201:0.168184:0.816138:0.116944:0.816138:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x h:@0.321990:0.839648:0.364189:0.839648:0.364189:0.824611:0.321990:0.824611:0.000000:0.000000:0.000000:0.000000:0.000000
(  +  ) –  ( ):@0.325913:0.839542:0.408392:0.839542:0.408392:0.824479:0.325913:0.824479:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.386774:0.839648:0.402957:0.839648:0.402957:0.824611:0.386774:0.824611:0.000000:0.000000:0.000000
h:@0.360899:0.854565:0.369483:0.854565:0.369483:0.839529:0.360899:0.839529:0.000000
h:@0.292927:0.851424:0.298525:0.851424:0.298525:0.841618:0.292927:0.841618:0.000000
→:@0.298525:0.850801:0.308338:0.850801:0.308338:0.841661:0.298525:0.841661:0.000000
0:@0.308335:0.851355:0.313394:0.851355:0.313394:0.841531:0.308335:0.841531:0.000000
lím:@0.292803:0.842855:0.312996:0.842855:0.312996:0.827818:0.292803:0.827818:0.000000:0.000000:0.000000
 ,:@0.410673:0.843779:0.416935:0.843779:0.416935:0.828716:0.410673:0.828716:0.000000:0.000000
se usa para definir la derivada de una función de   en  . Si el límite existe,:@0.116938:0.873879:0.580522:0.873879:0.580522:0.858816:0.116938:0.858816:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.432356:0.873984:0.436279:0.873984:0.436279:0.858948:0.432356:0.858948:0.000000
x:@0.459697:0.873984:0.466522:0.873984:0.466522:0.858948:0.459697:0.858948:0.000000
este   se denota con  ( ) o también con :@0.116938:0.900573:0.379625:0.900573:0.379625:0.885510:0.116938:0.885510:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.146331:0.900678:0.153349:0.900678:0.153349:0.885642:0.146331:0.885642:0.000000
f' x:@0.252449:0.900678:0.271519:0.900678:0.271519:0.885642:0.252449:0.885642:0.000000:0.000000:0.000000:0.000000
df:@0.382364:0.895354:0.395831:0.895354:0.395831:0.878885:0.382364:0.878885:0.000000:0.000000
dx:@0.380842:0.911692:0.397333:0.911692:0.397333:0.895223:0.380842:0.895223:0.000000:0.000000
 ( ). Esto se lee \  prima de  \.:@0.398559:0.900571:0.584046:0.900571:0.584046:0.885508:0.398559:0.885508:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.407706:0.900677:0.414531:0.900677:0.414531:0.885640:0.407706:0.885640:0.000000
f:@0.500896:0.900677:0.504818:0.900677:0.504818:0.885640:0.500896:0.885640:0.000000
x:@0.570290:0.900677:0.577115:0.900677:0.577115:0.885640:0.570290:0.885640:0.000000
f' x:@0.266141:0.932995:0.285209:0.932995:0.285209:0.917958:0.266141:0.917958:0.000000:0.000000:0.000000:0.000000
( ) = :@0.272984:0.932889:0.307935:0.932889:0.307935:0.917826:0.272984:0.917826:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x h:@0.342138:0.927870:0.384337:0.927870:0.384337:0.912833:0.342138:0.912833:0.000000:0.000000:0.000000:0.000000:0.000000
(  +  ) –  ( ):@0.346061:0.927765:0.428541:0.927765:0.428541:0.912701:0.346061:0.912701:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.406922:0.927870:0.423105:0.927870:0.423105:0.912833:0.406922:0.912833:0.000000:0.000000:0.000000
h:@0.381048:0.942788:0.389631:0.942788:0.389631:0.927751:0.381048:0.927751:0.000000
h:@0.314274:0.940564:0.319872:0.940564:0.319872:0.930758:0.314274:0.930758:0.000000
→:@0.319873:0.939941:0.329686:0.939941:0.329686:0.930801:0.319873:0.930801:0.000000
0:@0.329683:0.940495:0.334742:0.940495:0.334742:0.930672:0.329683:0.930672:0.000000
lím:@0.314412:0.931361:0.334605:0.931361:0.334605:0.916324:0.314412:0.916324:0.000000:0.000000:0.000000
 .:@0.430822:0.932892:0.437084:0.932892:0.437084:0.917829:0.430822:0.917829:0.000000:0.000000
 ©:@0.079553:0.731952:0.079553:0.720342:0.061505:0.720342:0.061505:0.731952:0.000000:0.000000
maya:@0.080774:0.720340:0.080774:0.684191:0.055786:0.684191:0.055786:0.720340:0.000000:0.000000:0.000000:0.000000
®EDUCACIÓN – Libro resuelto solo para fines didácticos – Prohibida su reproducción :@0.079553:0.684191:0.079553:0.268044:0.061505:0.268044:0.061505:0.684191:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000