178:@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
Ejemplo 2:@0.293660:0.140040:0.369443:0.140040:0.369443:0.123370:0.293660:0.123370:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
. Encontremos dónde crece y dónde decrece la función  ( ) = ( 2)  ( +3).:@0.369332:0.140040:0.901913:0.140040:0.901913:0.123606:0.369332:0.123606:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f  x:@0.774145:0.140040:0.794282:0.140040:0.794282:0.123634:0.774145:0.123634:0.000000:0.000000:0.000000:0.000000
x:@0.822593:0.140040:0.830047:0.140040:0.830047:0.123634:0.822593:0.123634:0.000000
–:@0.829974:0.140622:0.839177:0.140622:0.839177:0.122968:0.829974:0.122968:0.000000
2:@0.852785:0.133976:0.858022:0.133976:0.858022:0.124395:0.852785:0.124395:0.000000
x:@0.866718:0.140040:0.874173:0.140040:0.874173:0.123634:0.866718:0.123634:0.000000
Lo primero que debemos hacer es hallar   ´( ), para lo cual tenemos que aplicar las reglas :@0.293645:0.167402:0.931145:0.167402:0.931145:0.150968:0.293645:0.150968:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.587020:0.167402:0.612882:0.167402:0.612882:0.150996:0.587020:0.150996:0.000000:0.000000:0.000000
para derivar un producto y la regla de potencias.:@0.293627:0.184044:0.643775:0.184044:0.643775:0.167610:0.293627:0.167610:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Empecemos por aplicar las reglas de las derivadas. :@0.293627:0.211406:0.661254:0.211406:0.661254:0.194972:0.293627:0.194972:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ahora, resolvemos la ecuación  ´( ) = 0. :@0.293660:0.268129:0.582848:0.268129:0.582848:0.251695:0.293660:0.251695:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f  x:@0.517594:0.268129:0.543162:0.268129:0.543162:0.251723:0.517594:0.251723:0.000000:0.000000:0.000000:0.000000
3:@0.293652:0.295491:0.302634:0.295491:0.302634:0.279057:0.293652:0.279057:0.000000
x:@0.302561:0.295491:0.310016:0.295491:0.310016:0.279085:0.302561:0.279085:0.000000
2:@0.309951:0.289428:0.315187:0.289428:0.315187:0.279847:0.309951:0.279847:0.000000
–:@0.315141:0.296075:0.324345:0.296075:0.324345:0.278420:0.315141:0.278420:0.000000
 2    8 = 0.:@0.324253:0.295492:0.401343:0.295492:0.401343:0.279058:0.324253:0.279058:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.337101:0.295492:0.344556:0.295492:0.344556:0.279086:0.337101:0.279086:0.000000
–:@0.348440:0.296075:0.357644:0.296075:0.357644:0.278420:0.348440:0.278420:0.000000
(3x + 4)(x   2) = 0, es decir:   = :@0.293660:0.324934:0.515044:0.324934:0.515044:0.308501:0.293660:0.308501:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
–:@0.364234:0.325517:0.373437:0.325517:0.373437:0.307863:0.364234:0.307863:0.000000
x:@0.488777:0.324934:0.496232:0.324934:0.496232:0.308528:0.488777:0.308528:0.000000
 ,2. :@0.537357:0.324936:0.560589:0.324936:0.560589:0.308502:0.537357:0.308502:0.000000:0.000000:0.000000:0.000000:0.000000
 Como   es continua, entonces no hay más puntos críticos.:@0.293660:0.352299:0.715170:0.352299:0.715170:0.335865:0.293660:0.335865:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.346286:0.352299:0.350980:0.352299:0.350980:0.335893:0.346286:0.335893:0.000000
Estos puntos críticos determinan los intervalos :@0.293660:0.386567:0.634082:0.386567:0.634082:0.370133:0.293660:0.370133:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
  y (2,∞).:@0.797535:0.386570:0.855334:0.386570:0.855334:0.370136:0.797535:0.370136:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Con la ayuda de una tabla podemos validar el signo de en los anteriores intervalos al :@0.293660:0.424654:0.930669:0.424654:0.930669:0.408220:0.293660:0.408220:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tomar algunos valores de prueba y, luego, concluimos (ver Figura 3.2).:@0.293660:0.441296:0.798142:0.441296:0.798142:0.424862:0.293660:0.424862:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Intervalo:@0.405856:0.490367:0.477171:0.490367:0.477171:0.473420:0.405856:0.473420:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Valor de :@0.525098:0.482046:0.593773:0.482046:0.593773:0.465099:0.525098:0.465099:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
prueba:@0.529000:0.498688:0.586044:0.498688:0.586044:0.481741:0.529000:0.481741:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Signo de :@0.633240:0.482046:0.706187:0.482046:0.706187:0.465099:0.633240:0.465099:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.652458:0.498688:0.677657:0.498688:0.677657:0.481741:0.652458:0.481741:0.000000:0.000000:0.000000
´( ):@0.658053:0.498688:0.683124:0.498688:0.683124:0.481741:0.658053:0.481741:0.000000:0.000000:0.000000:0.000000
Conclusión:@0.739432:0.490367:0.826975:0.490367:0.826975:0.473420:0.739432:0.473420:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.535377:0.539435:0.542832:0.539435:0.542832:0.523029:0.535377:0.523029:0.000000
 =  2:@0.542765:0.539435:0.579654:0.539435:0.579654:0.523001:0.542765:0.523001:0.000000:0.000000:0.000000:0.000000:0.000000
–:@0.561559:0.540017:0.570763:0.540017:0.570763:0.522363:0.561559:0.522363:0.000000
f:@0.617573:0.539435:0.622266:0.539435:0.622266:0.523029:0.617573:0.523029:0.000000
´( 2) = 8>0:@0.622193:0.539435:0.702853:0.539435:0.702853:0.523001:0.622193:0.523001:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
–:@0.632427:0.540017:0.641631:0.540017:0.641631:0.522363:0.632427:0.522363:0.000000
crece:@0.763616:0.537826:0.802816:0.537826:0.802816:0.521392:0.763616:0.521392:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.539934:0.588167:0.547389:0.588167:0.547389:0.571760:0.539934:0.571760:0.000000
 = 0:@0.547322:0.588167:0.575117:0.588167:0.575117:0.571733:0.547322:0.571733:0.000000:0.000000:0.000000:0.000000
f:@0.617564:0.589775:0.622258:0.589775:0.622258:0.573369:0.617564:0.573369:0.000000
´(0) =  8<0:@0.622184:0.589775:0.702808:0.589775:0.702808:0.573341:0.622184:0.573341:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
–:@0.664908:0.590358:0.674111:0.590358:0.674111:0.572704:0.664908:0.572704:0.000000
decrece:@0.754220:0.588167:0.812215:0.588167:0.812215:0.571733:0.754220:0.571733:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.539934:0.631490:0.547389:0.631490:0.547389:0.615083:0.539934:0.615083:0.000000
 = 3:@0.547322:0.631490:0.575117:0.631490:0.575117:0.615056:0.547322:0.615056:0.000000:0.000000:0.000000:0.000000
f:@0.617564:0.631490:0.622258:0.631490:0.622258:0.615083:0.617564:0.615083:0.000000
´(3) = 13>0:@0.622184:0.631490:0.702661:0.631490:0.702661:0.615056:0.622184:0.615056:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
crece:@0.763607:0.631490:0.802807:0.631490:0.802807:0.615056:0.763607:0.615056:0.000000:0.000000:0.000000:0.000000:0.000000
Figura 3.2:@0.581712:0.674940:0.638906:0.674940:0.638906:0.661494:0.581712:0.661494:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.642394:0.857743:0.648961:0.857743:0.648961:0.846151:0.642394:0.846151:0.000000
4:@0.696441:0.857743:0.703009:0.857743:0.703009:0.846151:0.696441:0.846151:0.000000
6:@0.749068:0.857743:0.755635:0.857743:0.755635:0.846151:0.749068:0.846151:0.000000
-2:@0.530906:0.857743:0.541404:0.857743:0.541404:0.846151:0.530906:0.846151:0.000000:0.000000
-4:@0.477563:0.857743:0.488060:0.857743:0.488060:0.846151:0.477563:0.846151:0.000000:0.000000
-6:@0.421378:0.857743:0.431875:0.857743:0.431875:0.846151:0.421378:0.846151:0.000000:0.000000
0:@0.581933:0.857743:0.588500:0.857743:0.588500:0.846151:0.581933:0.846151:0.000000
10:@0.575571:0.793085:0.588705:0.793085:0.588705:0.781492:0.575571:0.781492:0.000000:0.000000
20:@0.575571:0.734860:0.588705:0.734860:0.588705:0.723267:0.575571:0.723267:0.000000:0.000000
y:@0.565545:0.710212:0.572445:0.710212:0.572445:0.696031:0.565545:0.696031:0.000000
x:@0.765660:0.865460:0.772560:0.865460:0.772560:0.851279:0.765660:0.851279:0.000000
(2,0):@0.602331:0.868629:0.632850:0.868629:0.632850:0.853172:0.602331:0.853172:0.000000:0.000000:0.000000:0.000000:0.000000
(-1.33333, 18,51852):@0.413823:0.727710:0.555816:0.727710:0.555816:0.712252:0.413823:0.712252:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y=  x:@0.713904:0.711413:0.744321:0.711413:0.744321:0.697232:0.713904:0.697232:0.000000:0.000000:0.000000:0.000000:0.000000
( -2) ( +3):@0.732977:0.711413:0.804013:0.711413:0.804013:0.697243:0.732977:0.697243:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2 :@0.761593:0.707662:0.770874:0.707662:0.770874:0.696069:0.761593:0.696069:0.000000:0.000000
x:@0.775318:0.711413:0.782218:0.711413:0.782218:0.697232:0.775318:0.697232:0.000000
DBA 8 (Ev. 2) Relaciona características algebraicas de las funciones, sus gráficas y procesos de aproximación sucesiva.:@0.305017:0.971366:0.916107:0.971366:0.916107:0.959414:0.305017:0.959414:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
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