183:@0.937671:0.974518:0.968375:0.974518:0.968375:0.956333:0.937671:0.956333:0.000000:0.000000:0.000000
Pensamiento espacial, numérico y variacional:@0.522009:0.043661:0.926913:0.043661:0.926913:0.024916:0.522009:0.024916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5.  Intervalos de crecimiento y decrecimiento::@0.073089:0.136836:0.425256:0.136836:0.425256:0.120167:0.073089:0.120167:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Creciente en donde :@0.103214:0.167527:0.251378:0.167527:0.251378:0.151093:0.103214:0.151093:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x x :@0.103210:0.194633:0.135226:0.194633:0.135226:0.178226:0.103210:0.178226:0.000000:0.000000:0.000000:0.000000
2:@0.110598:0.188569:0.115835:0.188569:0.115835:0.178988:0.110598:0.178988:0.000000
 (:@0.115788:0.194633:0.124624:0.194633:0.124624:0.178199:0.115788:0.178199:0.000000:0.000000
–:@0.135171:0.195215:0.144375:0.195215:0.144375:0.177561:0.135171:0.177561:0.000000
 2)( + 2) > 0      (1)     :@0.144283:0.194633:0.296143:0.194633:0.296143:0.178199:0.144283:0.178199:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x :@0.166721:0.194633:0.177416:0.194633:0.177416:0.178226:0.166721:0.178226:0.000000:0.000000
Decreciente en donde  :@0.103198:0.221745:0.273831:0.221745:0.273831:0.205311:0.103198:0.205311:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x x :@0.103210:0.248853:0.135226:0.248853:0.135226:0.232447:0.103210:0.232447:0.000000:0.000000:0.000000:0.000000
2:@0.110598:0.242790:0.115835:0.242790:0.115835:0.233209:0.110598:0.233209:0.000000
 (:@0.115788:0.248853:0.124624:0.248853:0.124624:0.232420:0.115788:0.232420:0.000000:0.000000
–:@0.135171:0.249436:0.144375:0.249436:0.144375:0.231782:0.135171:0.231782:0.000000
 2)( + 2) < 0     (2).:@0.144283:0.248853:0.275158:0.248853:0.275158:0.232420:0.144283:0.232420:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x :@0.166721:0.248853:0.177416:0.248853:0.177416:0.232447:0.166721:0.232447:0.000000:0.000000
En la recta real representamos los puntos de separación  2,0,2 (números que anulan :@0.103198:0.275966:0.710273:0.275966:0.710273:0.259532:0.103198:0.259532:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
–:@0.505893:0.276548:0.515097:0.276548:0.515097:0.258894:0.505893:0.258894:0.000000
los factores en las desigualdades (1) y (2)) y tomamos puntos de prueba en los :@0.103198:0.292358:0.710689:0.292358:0.710689:0.275924:0.103198:0.275924:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
intervalos ( ∞ , 2),( 2,0),(0,2) y (2,∞) para obtener el signo de  ´( ) en dichos :@0.103198:0.308750:0.710361:0.308750:0.710361:0.292316:0.103198:0.292316:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
–:@0.189601:0.309333:0.198805:0.309333:0.198805:0.291678:0.189601:0.291678:0.000000
–:@0.222606:0.309333:0.231809:0.309333:0.231809:0.291678:0.222606:0.291678:0.000000
–:@0.255463:0.309333:0.264666:0.309333:0.264666:0.291678:0.255463:0.291678:0.000000
f x:@0.594800:0.308750:0.618288:0.308750:0.618288:0.292344:0.594800:0.292344:0.000000:0.000000:0.000000
intervalos.:@0.103216:0.325142:0.176897:0.325142:0.176897:0.308709:0.103216:0.308709:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
La solución se presenta en la gráfica de la Figura 3.5.:@0.103216:0.352255:0.478886:0.352255:0.478886:0.335821:0.103216:0.335821:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Figura 3.5:@0.361141:0.378977:0.418335:0.378977:0.418335:0.365532:0.361141:0.365532:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.658276:0.453242:0.666941:0.453242:0.666941:0.435430:0.658276:0.435430:0.000000
f’’(x) < 0:@0.230254:0.434117:0.292104:0.434117:0.292104:0.416305:0.230254:0.416305:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f’’(x) > 0 f’’(x) < 0:@0.363619:0.434117:0.495131:0.434117:0.495131:0.416305:0.363619:0.416305:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f’’(x) > 0:@0.540450:0.434117:0.602300:0.434117:0.602300:0.416305:0.540450:0.416305:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
0:@0.426286:0.455355:0.434533:0.455355:0.434533:0.440794:0.426286:0.440794:0.000000
-√2:@0.357692:0.456179:0.379908:0.456179:0.379908:0.441617:0.357692:0.441617:0.000000:0.000000:0.000000
√2:@0.472680:0.456179:0.489961:0.456179:0.489961:0.441617:0.472680:0.441617:0.000000:0.000000
Cóncava:@0.241365:0.462737:0.283838:0.462737:0.283838:0.451223:0.241365:0.451223:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
hacia abajo:@0.234876:0.474043:0.290327:0.474043:0.290327:0.462530:0.234876:0.462530:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Cóncava:@0.440226:0.462737:0.482699:0.462737:0.482699:0.451223:0.440226:0.451223:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
hacia abajo:@0.433737:0.474043:0.489188:0.474043:0.489188:0.462530:0.433737:0.462530:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Cóncava:@0.372347:0.463189:0.414820:0.463189:0.414820:0.451675:0.372347:0.451675:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
hacia arriba:@0.365333:0.474496:0.421834:0.474496:0.421834:0.462982:0.365333:0.462982:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Cóncava:@0.552753:0.463189:0.595226:0.463189:0.595226:0.451675:0.552753:0.451675:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
hacia arriba:@0.545739:0.474496:0.602240:0.474496:0.602240:0.462982:0.545739:0.462982:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
6.  Valores extremos: máximos y mínimos.:@0.073089:0.517101:0.396350:0.517101:0.396350:0.500431:0.073089:0.500431:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Al aplicar el criterio de la primera derivada y con base en la gráfica anterior, :@0.103214:0.541967:0.710377:0.541967:0.710377:0.525533:0.103214:0.525533:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
concluimos que en   = -2 hay un máximo relativo y en   = 2 hay un mínimo relativo.:@0.103214:0.558608:0.706486:0.558608:0.706486:0.542175:0.103214:0.542175:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.246183:0.558608:0.253638:0.558608:0.253638:0.542202:0.246183:0.542202:0.000000
x:@0.497810:0.558608:0.505265:0.558608:0.505265:0.542202:0.497810:0.542202:0.000000
7.  Análisis de la concavidad y puntos de inflexión::@0.073089:0.593115:0.458782:0.593115:0.458782:0.576445:0.073089:0.576445:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Hallamos la segunda derivada de la función.:@0.103214:0.617981:0.422205:0.617981:0.422205:0.601547:0.103214:0.601547:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Concavidad hacia arriba en donde  :@0.103210:0.689309:0.359871:0.689309:0.359871:0.672875:0.103210:0.672875:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Concavidad hacia abajo en donde  :@0.103210:0.724154:0.358725:0.724154:0.358725:0.707720:0.103210:0.707720:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ahora, te invitamos a solucionar las desigualdades obtenidas.:@0.103210:0.751517:0.545985:0.751517:0.545985:0.735084:0.103210:0.735084:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Para hallar los puntos de inflexión solucionamos la ecuación  ”( ) = 0:@0.103210:0.778881:0.598880:0.778881:0.598880:0.762447:0.103210:0.762447:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f  x:@0.540916:0.778881:0.566355:0.778881:0.566355:0.762475:0.540916:0.762475:0.000000:0.000000:0.000000:0.000000
Entonces :@0.103210:0.842674:0.174328:0.842674:0.174328:0.826241:0.103210:0.826241:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
. :@0.314248:0.842674:0.321482:0.842674:0.321482:0.826241:0.314248:0.826241:0.000000:0.000000
Evaluamos  ”( ) para estos valores::@0.103210:0.870038:0.351159:0.870038:0.351159:0.853604:0.103210:0.853604:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f  x:@0.185380:0.870038:0.210819:0.870038:0.210819:0.853632:0.185380:0.853632:0.000000:0.000000:0.000000:0.000000
Y concluimos que los puntos de inflexión son :@0.103210:0.933550:0.416071:0.933550:0.416071:0.917116:0.103210:0.917116:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
.:@0.702351:0.933550:0.705554:0.933550:0.705554:0.917116:0.702351:0.917116:0.000000
15:@0.412484:0.804416:0.430376:0.804416:0.430376:0.787982:0.412484:0.787982:0.000000:0.000000
4:@0.417226:0.819425:0.426209:0.819425:0.426209:0.802991:0.417226:0.802991:0.000000
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