170:@0.031627:0.974518:0.062330:0.974518:0.062330:0.956333:0.031627:0.956333:0.000000:0.000000:0.000000
Aplicaciones de la derivada:@0.073089:0.043661:0.316384:0.043661:0.316384:0.024916:0.073089:0.024916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
El cálculo se construye sobre el concepto de límite y el concepto de función. Determinar :@0.293660:0.280382:0.931151:0.280382:0.931151:0.263948:0.293660:0.263948:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
el comportamiento de las funciones es una parte a la que el cálculo le dedica varias :@0.293660:0.297024:0.931090:0.297024:0.931090:0.280590:0.293660:0.280590:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
secciones con el fin de dar repuesta a interrogantes como ¿dónde crece la función? ¿La :@0.293660:0.313666:0.931078:0.313666:0.931078:0.297232:0.293660:0.297232:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
función es decreciente? ¿Tiene valores extremos? ¿Tiene valores máximos? ¿Tiene valores :@0.293660:0.330308:0.930455:0.330308:0.930455:0.313874:0.293660:0.313874:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
mínimos? Todas estas preguntas las podemos resolver gracias a la aplicación del :@0.293660:0.346949:0.931063:0.346949:0.931063:0.330516:0.293660:0.330516:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
concepto de derivada de una función. Ya en el mundo de las aplicaciones estas preguntas :@0.293660:0.363591:0.931481:0.363591:0.931481:0.347157:0.293660:0.347157:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
adquieren mayor relevancia.:@0.293660:0.380233:0.498424:0.380233:0.498424:0.363799:0.293660:0.363799:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Antes de empezar, y con base en la gráfica de la Figura 2.1, exploremos el :@0.403441:0.434957:0.931273:0.434957:0.931273:0.418523:0.403441:0.418523:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
comportamiento de la función  =  + :@0.403441:0.453693:0.687100:0.453699:0.687100:0.437265:0.403441:0.437259:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y  x:@0.633182:0.453693:0.666996:0.453693:0.666996:0.437287:0.633182:0.437287:0.000000:0.000000:0.000000:0.000000
3:@0.666946:0.447635:0.672183:0.447635:0.672183:0.438054:0.666946:0.438054:0.000000
3:@0.693017:0.445613:0.700367:0.445613:0.700367:0.432167:0.693017:0.432167:0.000000
2:@0.693017:0.459479:0.700367:0.459479:0.700367:0.446033:0.693017:0.446033:0.000000
   e intentemos responder las :@0.705876:0.453699:0.930829:0.453699:0.930829:0.437265:0.705876:0.437265:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.710256:0.453699:0.717711:0.453699:0.717711:0.437293:0.710256:0.437293:0.000000
2:@0.717673:0.447635:0.722910:0.447635:0.722910:0.438054:0.717673:0.438054:0.000000
siguientes preguntas: ¿cuál es el dominio de la función? ¿La función es :@0.403443:0.470341:0.931151:0.470341:0.931151:0.453907:0.403443:0.453907:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
continua? ¿La función es derivable en todo su domino? ¿En qué intervalos :@0.403443:0.486983:0.930925:0.486983:0.930925:0.470549:0.403443:0.470549:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la función es creciente? ¿En qué intervalo la función decrece? ¿Qué se :@0.403443:0.503625:0.930884:0.503625:0.930884:0.487191:0.403443:0.487191:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
puede decir de los puntos y de la gráfica?:@0.403443:0.520267:0.703389:0.520267:0.703389:0.503833:0.403443:0.503833:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ahora, y para empezar propiamente con el tema de máximos y mínimos, :@0.403443:0.547629:0.931278:0.547629:0.931278:0.531195:0.403443:0.531195:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
precisemos algunas definiciones: :@0.403443:0.564270:0.646319:0.564270:0.646319:0.547837:0.403443:0.547837:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Tema 2. Máximos y mínimos:@0.073089:0.098522:0.489257:0.098522:0.489257:0.067281:0.073089:0.067281:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Considera la siguiente función simple:  ( ) = :@0.293660:0.166113:0.583712:0.166113:0.583712:0.151173:0.293660:0.151173:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.546897:0.166113:0.562242:0.166113:0.562242:0.151199:0.546897:0.151199:0.000000:0.000000:0.000000
x b.:@0.583611:0.166113:0.606105:0.166113:0.606105:0.151199:0.583611:0.151199:0.000000:0.000000:0.000000:0.000000
2:@0.590343:0.160601:0.595104:0.160601:0.595104:0.151891:0.590343:0.151891:0.000000
¿Cuál crees que es el valor más bajo (mínimo) que puede alcanzar esta función?  :@0.293667:0.184810:0.824699:0.184810:0.824699:0.169870:0.293667:0.169870:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Tiene un valor más alto (máximo)?:@0.293667:0.199939:0.525436:0.199939:0.525436:0.184999:0.293667:0.184999:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Reto matemático:@0.302768:0.139600:0.437491:0.139600:0.437491:0.122653:0.302768:0.122653:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.135431:0.426306:0.140616:0.426306:0.140616:0.415651:0.135431:0.415651:0.000000
x:@0.362721:0.615538:0.367905:0.615538:0.367905:0.604882:0.362721:0.604882:0.000000
y  x:@0.310330:0.422793:0.332339:0.422793:0.332339:0.412137:0.310330:0.412137:0.000000:0.000000:0.000000:0.000000
 =:@0.315515:0.422793:0.325014:0.422793:0.325014:0.412146:0.315515:0.412146:0.000000:0.000000
3:@0.332339:0.419974:0.337071:0.419974:0.337071:0.411256:0.332339:0.411256:0.000000
 :@0.337071:0.419974:0.339110:0.419974:0.339110:0.411263:0.337071:0.411263:0.000000
 + :@0.339109:0.422793:0.351101:0.422793:0.351101:0.412146:0.339109:0.412146:0.000000:0.000000:0.000000
3:@0.353217:0.416645:0.359248:0.416645:0.359248:0.405999:0.353217:0.405999:0.000000
2:@0.353217:0.428727:0.359248:0.428727:0.359248:0.418080:0.353217:0.418080:0.000000
x:@0.364983:0.423028:0.370168:0.423028:0.370168:0.412373:0.364983:0.412373:0.000000
2:@0.370167:0.420210:0.374900:0.420210:0.374900:0.411492:0.370167:0.411492:0.000000
6:@0.145113:0.454554:0.150047:0.454554:0.150047:0.445843:0.145113:0.445843:0.000000
4:@0.146045:0.502464:0.150980:0.502464:0.150980:0.493753:0.146045:0.493753:0.000000
2:@0.146344:0.551584:0.151278:0.551584:0.151278:0.542873:0.146344:0.542873:0.000000
-2:@0.143795:0.647911:0.151682:0.647911:0.151682:0.639200:0.143795:0.639200:0.000000:0.000000
0:@0.146700:0.605234:0.151634:0.605234:0.151634:0.596523:0.146700:0.596523:0.000000
1:@0.077568:0.605234:0.082503:0.605234:0.082503:0.596523:0.077568:0.596523:0.000000
1:@0.226576:0.605234:0.231510:0.605234:0.231510:0.596523:0.226576:0.596523:0.000000
3:@0.371793:0.605234:0.376728:0.605234:0.376728:0.596523:0.371793:0.596523:0.000000
2:@0.301469:0.605234:0.306403:0.605234:0.306403:0.596523:0.301469:0.596523:0.000000
(0,0):@0.121864:0.590244:0.144962:0.590244:0.144962:0.578630:0.121864:0.578630:0.000000:0.000000:0.000000:0.000000:0.000000
(1, -0.5):@0.179293:0.622855:0.218281:0.622855:0.218281:0.611240:0.179293:0.611240:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Figura 2.1:@0.073089:0.681101:0.130283:0.681101:0.130283:0.667655:0.073089:0.667655:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Definición 1::@0.333979:0.705660:0.428883:0.705660:0.428883:0.688991:0.333979:0.688991:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sea la función definida en un intervalo  ;   :@0.333979:0.733022:0.646166:0.733022:0.646166:0.716589:0.333979:0.716589:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
D c:@0.616033:0.733022:0.642208:0.733022:0.642208:0.716616:0.616033:0.716616:0.000000:0.000000:0.000000
[:@0.646092:0.732884:0.661425:0.732884:0.661425:0.718835:0.646092:0.718835:0.000000
D:@0.661333:0.733022:0.672856:0.733022:0.672856:0.716616:0.661333:0.716616:0.000000
.:@0.672783:0.733022:0.675985:0.733022:0.675985:0.716589:0.672783:0.716589:0.000000
a.    ( ) es el :@0.365524:0.760387:0.461770:0.760387:0.461770:0.743953:0.365524:0.743953:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f c:@0.399683:0.760387:0.416764:0.760387:0.416764:0.743981:0.399683:0.743981:0.000000:0.000000:0.000000
valor máximo:@0.461641:0.760387:0.569653:0.760387:0.569653:0.743440:0.461641:0.743440:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 de f en D, si  ( )≥f( ) x D.:@0.569545:0.760387:0.766551:0.760387:0.766551:0.743953:0.569545:0.743953:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f c:@0.660348:0.760387:0.677430:0.760387:0.677430:0.743981:0.660348:0.743981:0.000000:0.000000:0.000000
x:@0.702574:0.760387:0.710029:0.760387:0.710029:0.743981:0.702574:0.743981:0.000000
 :@0.714760:0.760969:0.719361:0.760969:0.719361:0.743315:0.714760:0.743315:0.000000
[:@0.736823:0.760248:0.752156:0.760248:0.752156:0.746200:0.736823:0.746200:0.000000
b.    ( ) es el :@0.365524:0.785249:0.461770:0.785249:0.461770:0.768815:0.365524:0.768815:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f c:@0.399683:0.785249:0.416764:0.785249:0.416764:0.768843:0.399683:0.768843:0.000000:0.000000:0.000000
valor mínimo :@0.461641:0.785249:0.570187:0.785249:0.570187:0.768302:0.461641:0.768302:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de f en D, si  ( )≤f( ) x D.:@0.570079:0.785249:0.763132:0.785249:0.763132:0.768815:0.570079:0.768815:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f c:@0.656942:0.785249:0.674024:0.785249:0.674024:0.768843:0.656942:0.768843:0.000000:0.000000:0.000000
x:@0.699169:0.785249:0.706624:0.785249:0.706624:0.768843:0.699169:0.768843:0.000000
 :@0.711354:0.785831:0.715956:0.785831:0.715956:0.768177:0.711354:0.768177:0.000000
[:@0.733404:0.785110:0.748738:0.785110:0.748738:0.771062:0.733404:0.771062:0.000000
El valor máximo y el valor mínimo de en se llaman :@0.333985:0.810114:0.702602:0.810114:0.702602:0.793681:0.333985:0.793681:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
valores extremos :@0.702425:0.810114:0.841037:0.810114:0.841037:0.793167:0.702425:0.793167:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de la :@0.841160:0.810114:0.880368:0.810114:0.880368:0.793681:0.841160:0.793681:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
función en ese intervalo.:@0.333967:0.826756:0.511411:0.826756:0.511411:0.810322:0.333967:0.810322:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Algunas veces, el valor máximo suele llamarse también máximo absoluto y el valor :@0.293655:0.876612:0.930990:0.876612:0.930990:0.860179:0.293655:0.860179:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
mínimo también se denomina mínimo absoluto.:@0.293655:0.893254:0.646270:0.893254:0.646270:0.876820:0.293655:0.876820:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
La existencia de valores extremos depende del intervalo donde esté definida la función.:@0.293655:0.920616:0.927386:0.920616:0.927386:0.904182:0.293655:0.904182:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Respuesta para quinta tinta: la función  ( ) =   tiene un mínimo en x=0, ya que f(0)=0 es el valor más bajo que la :@0.293660:0.215251:0.905880:0.215251:0.905880:0.203299:0.293660:0.203299:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.504199:0.215251:0.516636:0.215251:0.516636:0.203319:0.504199:0.203319:0.000000:0.000000:0.000000
x:@0.535083:0.215251:0.540505:0.215251:0.540505:0.203319:0.535083:0.203319:0.000000
2:@0.540535:0.210841:0.544343:0.210841:0.544343:0.203873:0.540535:0.203873:0.000000
función puede alcanzar. No tiene un máximo, porque a medida que x crece o se aleja en cualquier dirección,  ( ) se :@0.293662:0.227354:0.906108:0.227354:0.906108:0.215402:0.293662:0.215402:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.872828:0.227354:0.885117:0.227354:0.885117:0.215422:0.872828:0.215422:0.000000:0.000000:0.000000
hace cada vez más grande sin límite.:@0.293648:0.239457:0.485611:0.239457:0.485611:0.227505:0.293648:0.227505:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
MUESTRA EDITORIAL:@0.248902:0.947499:0.888171:0.113285:0.743922:0.050540:0.104653:0.884754:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 Muestra editorial solo para fines didácticos – Prohibida su venta:@0.095585:0.659700:0.095585:0.341447:0.077558:0.341447:0.077558:0.659700:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000