153:@0.918240:0.966765:0.943652:0.966765:0.943652:0.950778:0.918240:0.950778:0.000000:0.000000:0.000000
Análisis de funciones polinomiales de grado ≤ 4:@0.108233:0.108020:0.488551:0.108020:0.488551:0.090337:0.108233:0.090337:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Definición :@0.108233:0.125190:0.195100:0.125190:0.195100:0.108244:0.108233:0.108244:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
. Sean      [ ].:@0.188319:0.124727:0.309160:0.124727:0.309160:0.108230:0.188319:0.108230:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.232899:0.124843:0.242165:0.124843:0.242165:0.108374:0.232899:0.108374:0.000000
:@0.246692:0.124511:0.262740:0.124511:0.262740:0.109864:0.246692:0.109864:0.000000
P:@0.267653:0.124843:0.276438:0.124843:0.276438:0.108374:0.267653:0.108374:0.000000
4:@0.276435:0.128005:0.281389:0.128005:0.281389:0.118387:0.276435:0.118387:0.000000
:@0.287244:0.123640:0.300549:0.123640:0.300549:0.110778:0.287244:0.110778:0.000000
i):@0.108224:0.149423:0.118762:0.149423:0.118762:0.132709:0.108224:0.132709:0.000000:0.000000
  Se dice que :@0.118762:0.149207:0.217093:0.149207:0.217093:0.132709:0.118762:0.132709:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.217093:0.149901:0.227053:0.149901:0.227053:0.132738:0.217093:0.132738:0.000000
 es par:@0.227053:0.149670:0.276640:0.149670:0.276640:0.132724:0.227053:0.132724:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 si y solo si se verifica la condición::@0.276640:0.149207:0.518203:0.149207:0.518203:0.132709:0.276640:0.132709:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p x:@0.271922:0.173802:0.305116:0.173802:0.305116:0.157333:0.271922:0.157333:0.000000:0.000000:0.000000
(– ) =  ( ),        .:@0.281188:0.173686:0.432058:0.173685:0.432058:0.157188:0.281188:0.157188:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p x:@0.330160:0.173802:0.352855:0.173802:0.352855:0.157333:0.330160:0.157333:0.000000:0.000000:0.000000
∀:@0.374008:0.181272:0.385581:0.181272:0.385581:0.162273:0.374008:0.162273:0.000000
x:@0.385587:0.173801:0.393062:0.173801:0.393062:0.157332:0.385587:0.157332:0.000000
:@0.397204:0.173167:0.411856:0.173167:0.411856:0.159794:0.397204:0.159794:0.000000
:@0.415998:0.172599:0.429303:0.172599:0.429303:0.159736:0.415998:0.159736:0.000000
ii):@0.108228:0.203326:0.123024:0.203326:0.123024:0.186612:0.108228:0.186612:0.000000:0.000000:0.000000
  Se dice que   :@0.123024:0.203110:0.231198:0.203110:0.231198:0.186612:0.123024:0.186612:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.217096:0.203804:0.227056:0.203804:0.227056:0.186641:0.217096:0.186641:0.000000
es impar:@0.231198:0.203573:0.297064:0.203573:0.297064:0.186627:0.231198:0.186627:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 si y solo si se verifica la condición::@0.297064:0.203110:0.538627:0.203110:0.538627:0.186612:0.297064:0.186612:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p x:@0.266685:0.227705:0.299879:0.227705:0.299879:0.211236:0.266685:0.211236:0.000000:0.000000:0.000000
(– ) = – ( ),        .:@0.275951:0.227589:0.437308:0.227585:0.437308:0.211087:0.275951:0.211091:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p x:@0.335423:0.227705:0.358118:0.227705:0.358118:0.211236:0.335423:0.211236:0.000000:0.000000:0.000000
∀:@0.379257:0.235171:0.390829:0.235171:0.390829:0.216172:0.379257:0.216172:0.000000
x:@0.390838:0.227700:0.398313:0.227700:0.398313:0.211232:0.390838:0.211232:0.000000
:@0.402454:0.227066:0.417106:0.227066:0.417106:0.213693:0.402454:0.213693:0.000000
:@0.421248:0.226498:0.434553:0.226498:0.434553:0.213636:0.421248:0.213636:0.000000
Ejercicios resueltos:@0.108238:0.257385:0.238893:0.257385:0.238893:0.240598:0.108238:0.240598:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1.:@0.108238:0.274576:0.120510:0.274576:0.120510:0.257862:0.108238:0.257862:0.000000:0.000000
  La función  , definida como  ( ) = –  + 5  –1,   :@0.120509:0.274360:0.487093:0.274356:0.487093:0.257859:0.120509:0.257862:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.211847:0.274476:0.221113:0.274476:0.221113:0.258007:0.211847:0.258007:0.000000
p x:@0.336682:0.274476:0.359376:0.274476:0.359376:0.258007:0.336682:0.258007:0.000000:0.000000:0.000000
x:@0.395306:0.274476:0.402781:0.274476:0.402781:0.258007:0.395306:0.258007:0.000000
4:@0.402831:0.268005:0.407784:0.268005:0.407784:0.258386:0.402831:0.258386:0.000000
x:@0.435756:0.274472:0.443231:0.274472:0.443231:0.258003:0.435756:0.258003:0.000000
2:@0.443244:0.268005:0.448197:0.268005:0.448197:0.258386:0.443244:0.258386:0.000000
∀:@0.487313:0.281943:0.498886:0.281943:0.498886:0.262944:0.487313:0.262944:0.000000
x:@0.498892:0.274472:0.506367:0.274472:0.506367:0.258003:0.498892:0.258003:0.000000
    , es una :@0.506367:0.274356:0.599895:0.274356:0.599895:0.257859:0.506367:0.257859:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.510708:0.273838:0.525360:0.273838:0.525360:0.260464:0.510708:0.260464:0.000000
:@0.529702:0.273269:0.543006:0.273269:0.543006:0.260407:0.529702:0.260407:0.000000
función par. En efecto,:@0.131982:0.291707:0.289242:0.291707:0.289242:0.275209:0.131982:0.275209:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.108247:0.309058:0.112389:0.309058:0.112389:0.292560:0.108247:0.292560:0.000000
p x:@0.152114:0.309173:0.185308:0.309173:0.185308:0.292705:0.152114:0.292705:0.000000:0.000000:0.000000
(– ) = –(– )  + 5(– )  – 1 = –  + 5  – 1 =  ( ),        .:@0.161381:0.309058:0.575648:0.309058:0.575648:0.292560:0.161381:0.292560:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.237305:0.309173:0.244780:0.309173:0.244780:0.292705:0.237305:0.292705:0.000000
4:@0.250714:0.302706:0.255667:0.302706:0.255667:0.293088:0.250714:0.293088:0.000000
x:@0.299706:0.309173:0.307181:0.309173:0.307181:0.292705:0.299706:0.292705:0.000000
2:@0.313133:0.302706:0.318086:0.302706:0.318086:0.293088:0.313133:0.293088:0.000000
x:@0.374958:0.309173:0.382433:0.309173:0.382433:0.292705:0.374958:0.292705:0.000000
4:@0.382431:0.302706:0.387384:0.302706:0.387384:0.293088:0.382431:0.293088:0.000000
x:@0.414973:0.309173:0.422448:0.309173:0.422448:0.292705:0.414973:0.292705:0.000000
2:@0.422446:0.302706:0.427399:0.302706:0.427399:0.293088:0.422446:0.293088:0.000000
p x:@0.473771:0.309173:0.496466:0.309173:0.496466:0.292705:0.473771:0.292705:0.000000:0.000000:0.000000
∀:@0.517598:0.316644:0.529171:0.316644:0.529171:0.297645:0.517598:0.297645:0.000000
x:@0.529177:0.309173:0.536652:0.309173:0.536652:0.292705:0.529177:0.292705:0.000000
:@0.540795:0.308539:0.555448:0.308539:0.555448:0.295166:0.540795:0.295166:0.000000
:@0.559588:0.307971:0.572893:0.307971:0.572893:0.295109:0.559588:0.295109:0.000000
2.:@0.108234:0.343976:0.120506:0.343976:0.120506:0.327262:0.108234:0.327262:0.000000:0.000000
  La función  , definida como  ( ) =   – 2 ,   :@0.120506:0.343759:0.451320:0.343759:0.451320:0.327262:0.120506:0.327262:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.212487:0.343875:0.221696:0.343875:0.221696:0.327406:0.212487:0.327406:0.000000
u x:@0.338204:0.343875:0.360841:0.343875:0.360841:0.327406:0.338204:0.327406:0.000000:0.000000:0.000000
x:@0.386914:0.343875:0.394389:0.343875:0.394389:0.327406:0.386914:0.327406:0.000000
3:@0.394389:0.337408:0.399342:0.337408:0.399342:0.327789:0.394389:0.327789:0.000000
x:@0.427643:0.343875:0.435118:0.343875:0.435118:0.327406:0.427643:0.327406:0.000000
∀:@0.451826:0.351346:0.463399:0.351346:0.463399:0.332347:0.451826:0.332347:0.000000
x:@0.463407:0.343875:0.470882:0.343875:0.470882:0.327406:0.463407:0.327406:0.000000
    , es una fun-:@0.470882:0.343759:0.595771:0.343759:0.595771:0.327262:0.470882:0.327262:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.475534:0.343241:0.490187:0.343241:0.490187:0.329867:0.475534:0.329867:0.000000
:@0.494838:0.342672:0.508143:0.342672:0.508143:0.329810:0.494838:0.329810:0.000000
ción impar. En efecto,:@0.131970:0.361110:0.283855:0.361110:0.283855:0.344612:0.131970:0.344612:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.108234:0.378461:0.112376:0.378461:0.112376:0.361963:0.108234:0.361963:0.000000
u x:@0.178746:0.378576:0.211882:0.378576:0.211882:0.362108:0.178746:0.362108:0.000000:0.000000:0.000000
(– ) = (– )  – 2(– ) = –(  – 2 ) = – ( ),        .:@0.187954:0.378461:0.549003:0.378461:0.549003:0.361963:0.187954:0.361963:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.253379:0.378576:0.260854:0.378576:0.260854:0.362108:0.253379:0.362108:0.000000
3:@0.266801:0.372109:0.271754:0.372109:0.271754:0.362491:0.266801:0.362491:0.000000
x:@0.315487:0.378576:0.322962:0.378576:0.322962:0.362108:0.315487:0.362108:0.000000
x:@0.364459:0.378576:0.371934:0.378576:0.371934:0.362108:0.364459:0.362108:0.000000
3:@0.371933:0.372109:0.376886:0.372109:0.376886:0.362491:0.371933:0.362491:0.000000
x:@0.404164:0.378576:0.411639:0.378576:0.411639:0.362108:0.404164:0.362108:0.000000
u x:@0.447183:0.378576:0.469820:0.378576:0.469820:0.362108:0.447183:0.362108:0.000000:0.000000:0.000000
∀:@0.490952:0.386047:0.502524:0.386047:0.502524:0.367048:0.490952:0.367048:0.000000
x:@0.502533:0.378576:0.510007:0.378576:0.510007:0.362108:0.502533:0.362108:0.000000
:@0.514149:0.377942:0.528801:0.377942:0.528801:0.364569:0.514149:0.364569:0.000000
:@0.532943:0.377374:0.546248:0.377374:0.546248:0.364512:0.532943:0.364512:0.000000
Definición :@0.108233:0.413625:0.195100:0.413625:0.195100:0.396679:0.108233:0.396679:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
. Sean      [ ],      , no vacío.:@0.188319:0.413162:0.432237:0.413162:0.432237:0.396665:0.188319:0.396665:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.232899:0.413278:0.242165:0.413278:0.242165:0.396809:0.232899:0.396809:0.000000
:@0.246692:0.412945:0.262740:0.412945:0.262740:0.398298:0.246692:0.398298:0.000000
P:@0.267653:0.413278:0.276438:0.413278:0.276438:0.396809:0.267653:0.396809:0.000000
4:@0.276435:0.416440:0.281389:0.416440:0.281389:0.406822:0.276435:0.406822:0.000000
:@0.287244:0.412075:0.300549:0.412075:0.300549:0.399213:0.287244:0.399213:0.000000
A:@0.313302:0.413278:0.324573:0.413278:0.324573:0.396809:0.313302:0.396809:0.000000
:@0.328715:0.412945:0.344763:0.412945:0.344763:0.398298:0.328715:0.398298:0.000000
:@0.348903:0.412075:0.362208:0.412075:0.362208:0.399213:0.348903:0.399213:0.000000
i):@0.108234:0.437858:0.118772:0.437858:0.118772:0.421144:0.108234:0.421144:0.000000:0.000000
  Se dice que   :@0.118772:0.437642:0.234788:0.437642:0.234788:0.421144:0.118772:0.421144:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.220686:0.438336:0.230646:0.438336:0.230646:0.421173:0.220686:0.421173:0.000000
es estrictamente creciente:@0.235963:0.438105:0.439998:0.438105:0.439998:0.421159:0.235963:0.421159:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 en el conjunto  si y :@0.439998:0.437642:0.599903:0.437642:0.599903:0.421144:0.439998:0.421144:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A :@0.555955:0.437758:0.571368:0.437758:0.571368:0.421289:0.555955:0.421289:0.000000:0.000000
solo si se verifica la condición::@0.131970:0.454993:0.343228:0.454993:0.343228:0.438495:0.131970:0.438495:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∀:@0.241260:0.487058:0.252833:0.487058:0.252833:0.468058:0.241260:0.468058:0.000000
u, v   A, u < v   p u:@0.252841:0.479587:0.405991:0.479587:0.405991:0.463118:0.252841:0.463118:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.280660:0.478952:0.295313:0.478952:0.295313:0.465579:0.280660:0.465579:0.000000
⇒:@0.358406:0.478965:0.377421:0.478965:0.377421:0.461253:0.358406:0.461253:0.000000
( ) <  ( ).:@0.390829:0.479471:0.462746:0.479471:0.462746:0.462973:0.390829:0.462973:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p v:@0.431036:0.479587:0.454039:0.479587:0.454039:0.463118:0.431036:0.463118:0.000000:0.000000:0.000000
ii):@0.108227:0.506090:0.123023:0.506090:0.123023:0.489375:0.108227:0.489375:0.000000:0.000000:0.000000
  Se dice que   :@0.123024:0.505873:0.232123:0.505873:0.232123:0.489375:0.123024:0.489375:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.218021:0.506567:0.227981:0.506567:0.227981:0.489404:0.218021:0.489404:0.000000
es creciente:@0.232412:0.506336:0.322860:0.506336:0.322860:0.489390:0.232412:0.489390:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 en el conjunto  si y solo si se verifica :@0.322862:0.505873:0.599933:0.505873:0.599933:0.489375:0.322862:0.489375:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A :@0.435275:0.505989:0.450687:0.505989:0.450687:0.489520:0.435275:0.489520:0.000000:0.000000
la condición::@0.131963:0.523224:0.221951:0.523224:0.221951:0.506726:0.131963:0.506726:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∀:@0.241260:0.551727:0.252833:0.551727:0.252833:0.532728:0.241260:0.532728:0.000000
u, v   A, u < v   p u:@0.252841:0.544256:0.405991:0.544256:0.405991:0.527787:0.252841:0.527787:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.280660:0.543622:0.295313:0.543622:0.295313:0.530248:0.280660:0.530248:0.000000
⇒:@0.358406:0.543634:0.377421:0.543634:0.377421:0.525922:0.358406:0.525922:0.000000
( ) ≤  ( ).:@0.390829:0.544140:0.462746:0.544140:0.462746:0.527643:0.390829:0.527643:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p v:@0.431036:0.544256:0.454039:0.544256:0.454039:0.527787:0.431036:0.527787:0.000000:0.000000:0.000000
iii):@0.108227:0.570759:0.127281:0.570759:0.127281:0.554045:0.108227:0.554045:0.000000:0.000000:0.000000:0.000000
 Se dice que   :@0.127281:0.570542:0.229983:0.570542:0.229983:0.554045:0.127281:0.554045:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.215880:0.571236:0.225841:0.571236:0.225841:0.554074:0.215880:0.554074:0.000000
es estrictamente decreciente:@0.229599:0.571005:0.449566:0.571005:0.449566:0.554059:0.229599:0.554059:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 en el conjunto  si y :@0.449566:0.570542:0.599897:0.570542:0.599897:0.554045:0.449566:0.554045:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A :@0.559128:0.570658:0.574540:0.570658:0.574540:0.554189:0.559128:0.554189:0.000000:0.000000
solo si se verifica la condición::@0.131963:0.587893:0.343226:0.587893:0.343226:0.571396:0.131963:0.571396:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∀:@0.241260:0.619959:0.252833:0.619959:0.252833:0.600960:0.241260:0.600960:0.000000
u, v   A, u < v   p u:@0.252841:0.612489:0.405991:0.612489:0.405991:0.596020:0.252841:0.596020:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.280660:0.611854:0.295313:0.611854:0.295313:0.598481:0.280660:0.598481:0.000000
⇒:@0.358406:0.611867:0.377421:0.611867:0.377421:0.594155:0.358406:0.594155:0.000000
( ) >  ( ).:@0.390829:0.612373:0.462746:0.612373:0.462746:0.595875:0.390829:0.595875:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p v:@0.431036:0.612489:0.454039:0.612489:0.454039:0.596020:0.431036:0.596020:0.000000:0.000000:0.000000
iv):@0.108227:0.638992:0.127030:0.638992:0.127030:0.622277:0.108227:0.622277:0.000000:0.000000:0.000000
 Se dice que   :@0.127029:0.638775:0.230387:0.638775:0.230387:0.622277:0.127029:0.622277:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.216285:0.639469:0.226245:0.639469:0.226245:0.622306:0.216285:0.622306:0.000000
es decreciente:@0.230098:0.639238:0.339003:0.639238:0.339003:0.622292:0.230098:0.622292:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 en el conjunto  si y solo si se verifi-:@0.339005:0.638775:0.595753:0.638775:0.595753:0.622277:0.339005:0.622277:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A :@0.449106:0.638891:0.464518:0.638891:0.464518:0.622422:0.449106:0.622422:0.000000:0.000000
ca la condición::@0.131942:0.656126:0.242002:0.656126:0.242002:0.639628:0.131942:0.639628:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∀:@0.241260:0.684629:0.252833:0.684629:0.252833:0.665629:0.241260:0.665629:0.000000
u, v   A, u < v   p u:@0.252841:0.677158:0.405991:0.677158:0.405991:0.660689:0.252841:0.660689:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.280660:0.676523:0.295313:0.676523:0.295313:0.663150:0.280660:0.663150:0.000000
⇒:@0.358406:0.676536:0.377421:0.676536:0.377421:0.658824:0.358406:0.658824:0.000000
( ) ≥  ( ).:@0.390829:0.677042:0.462746:0.677042:0.462746:0.660544:0.390829:0.660544:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p v:@0.431036:0.677158:0.454039:0.677158:0.454039:0.660689:0.431036:0.660689:0.000000:0.000000:0.000000
v):@0.108227:0.703661:0.122850:0.703661:0.122850:0.686947:0.108227:0.686947:0.000000:0.000000
  Se dice que   :@0.122850:0.703444:0.231852:0.703444:0.231852:0.686947:0.122850:0.686947:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.217749:0.704138:0.227709:0.704138:0.227709:0.686975:0.217749:0.686975:0.000000
es monótona:@0.232063:0.703907:0.332917:0.703907:0.332917:0.686961:0.232063:0.686961:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 en el conjunto  si allí   es creciente :@0.332917:0.703444:0.599876:0.703444:0.599876:0.686947:0.332917:0.686947:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A :@0.444991:0.703560:0.460403:0.703560:0.460403:0.687091:0.444991:0.687091:0.000000:0.000000
p:@0.498618:0.703560:0.507884:0.703560:0.507884:0.687091:0.498618:0.687091:0.000000
o decreciente. :@0.131942:0.720795:0.235435:0.720795:0.235435:0.704297:0.131942:0.704297:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
En cursos más avanzados se demuestra que una función   es estric-:@0.108207:0.755496:0.584438:0.755496:0.584438:0.738999:0.108207:0.738999:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.511038:0.755612:0.520304:0.755612:0.520304:0.739143:0.511038:0.739143:0.000000
tamente creciente en el conjunto   si y solo si             > 0,        .:@0.108207:0.779975:0.582627:0.779976:0.582627:0.763478:0.108207:0.763478:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.348770:0.780091:0.360041:0.780091:0.360041:0.763622:0.348770:0.763622:0.000000
∀:@0.526611:0.787563:0.538183:0.787563:0.538183:0.768563:0.526611:0.768563:0.000000
x:@0.538190:0.780092:0.545665:0.780092:0.545665:0.763623:0.538190:0.763623:0.000000
:@0.549808:0.779457:0.564460:0.779457:0.564460:0.766084:0.549808:0.766084:0.000000
A:@0.568601:0.780092:0.579872:0.780092:0.579872:0.763623:0.568601:0.763623:0.000000
De manera similar,   es estrictamente decreciente en el conjunto :@0.108239:0.804455:0.570909:0.804455:0.570909:0.787957:0.108239:0.787957:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.242730:0.804571:0.251996:0.804571:0.251996:0.788102:0.242730:0.788102:0.000000
A:@0.570909:0.804571:0.582180:0.804571:0.582180:0.788102:0.570909:0.788102:0.000000
si y solo si            < 0,        .:@0.108239:0.828934:0.322509:0.828933:0.322509:0.812435:0.108239:0.812436:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∀:@0.266493:0.836519:0.278066:0.836519:0.278066:0.817520:0.266493:0.817520:0.000000
x:@0.278074:0.829049:0.285549:0.829049:0.285549:0.812580:0.278074:0.812580:0.000000
:@0.289690:0.828414:0.304342:0.828414:0.304342:0.815041:0.289690:0.815041:0.000000
A:@0.308484:0.829049:0.319754:0.829049:0.319754:0.812580:0.308484:0.812580:0.000000
La función   es creciente en el conjunto   si y solo si:@0.108241:0.860540:0.480925:0.860540:0.480925:0.844042:0.108241:0.844042:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.187729:0.860656:0.196996:0.860656:0.196996:0.844187:0.187729:0.844187:0.000000
A:@0.395580:0.860656:0.406850:0.860656:0.406850:0.844187:0.395580:0.844187:0.000000
          ≥ 0,        ; y,   es decreciente en el conjunto   si y solo si:@0.108241:0.885019:0.573594:0.885019:0.573594:0.868521:0.108241:0.868522:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∀:@0.188278:0.892605:0.199850:0.892605:0.199850:0.873606:0.188278:0.873606:0.000000
x:@0.199859:0.885134:0.207334:0.885134:0.207334:0.868665:0.199859:0.868665:0.000000
:@0.211475:0.884500:0.226127:0.884500:0.226127:0.871127:0.211475:0.871127:0.000000
A:@0.230270:0.885134:0.241540:0.885134:0.241540:0.868665:0.230270:0.868665:0.000000
p:@0.262385:0.885134:0.271652:0.885134:0.271652:0.868665:0.262385:0.868665:0.000000
A:@0.488249:0.885134:0.499519:0.885134:0.499519:0.868665:0.488249:0.868665:0.000000
          ≤ 0,       :@0.108225:0.916626:0.230270:0.916626:0.230270:0.900128:0.108225:0.900128:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∀:@0.188278:0.924212:0.199850:0.924212:0.199850:0.905213:0.188278:0.905213:0.000000
x:@0.199859:0.916741:0.207334:0.916741:0.207334:0.900273:0.199859:0.900273:0.000000
:@0.211475:0.916107:0.226127:0.916107:0.226127:0.902734:0.211475:0.902734:0.000000
A.:@0.230270:0.916741:0.244777:0.916741:0.244777:0.900273:0.230270:0.900273:0.000000:0.000000
df x:@0.451047:0.772967:0.477942:0.772967:0.477942:0.756498:0.451047:0.756498:0.000000:0.000000:0.000000:0.000000
( ):@0.464514:0.772851:0.483895:0.772851:0.483895:0.756353:0.464514:0.756353:0.000000:0.000000:0.000000
dx:@0.459216:0.789305:0.475707:0.789305:0.475707:0.772837:0.459216:0.772837:0.000000:0.000000
df x:@0.109617:0.877354:0.136512:0.877354:0.136512:0.860885:0.109617:0.860885:0.000000:0.000000:0.000000:0.000000
( ):@0.123084:0.877238:0.142465:0.877238:0.142465:0.860741:0.123084:0.860741:0.000000:0.000000:0.000000
dx:@0.117786:0.893693:0.134277:0.893693:0.134277:0.877224:0.117786:0.877224:0.000000:0.000000
df x:@0.109617:0.908594:0.136512:0.908594:0.136512:0.892125:0.109617:0.892125:0.000000:0.000000:0.000000:0.000000
( ):@0.123084:0.908479:0.142465:0.908479:0.142465:0.891981:0.123084:0.891981:0.000000:0.000000:0.000000
dx:@0.117786:0.924933:0.134277:0.924933:0.134277:0.908464:0.117786:0.908464:0.000000:0.000000
df x:@0.187574:0.822377:0.214468:0.822377:0.214468:0.805909:0.187574:0.805909:0.000000:0.000000:0.000000:0.000000
( ):@0.201040:0.822262:0.220421:0.822262:0.220421:0.805764:0.201040:0.805764:0.000000:0.000000:0.000000
dx:@0.195743:0.838716:0.212234:0.838716:0.212234:0.822247:0.195743:0.822247:0.000000:0.000000
Interdisciplinariedad:@0.684804:0.499335:0.831589:0.499335:0.831589:0.483863:0.684804:0.483863:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Matemática y Física:@0.685042:0.528385:0.823260:0.528385:0.823260:0.512913:0.685042:0.512913:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Para resolver diversos proble-:@0.638498:0.543805:0.827644:0.543805:0.827644:0.528742:0.638498:0.528742:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
mas vinculados al movimien-:@0.638498:0.559647:0.827712:0.559647:0.827712:0.544584:0.638498:0.544584:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
to de los cuerpos, así como :@0.638498:0.575489:0.818847:0.575489:0.818847:0.560426:0.638498:0.560426:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
problemas de tipo geométrico :@0.638498:0.591331:0.839830:0.591331:0.839830:0.576268:0.638498:0.576268:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
en el ámbito de la óptica, utili-:@0.638498:0.607173:0.835399:0.607173:0.835399:0.592110:0.638498:0.592110:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
zamos el cálculo de derivadas y :@0.638498:0.623015:0.844599:0.623015:0.844599:0.607952:0.638498:0.607952:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
los valores máximos y mínimos :@0.638498:0.638857:0.844493:0.638857:0.844493:0.623794:0.638498:0.623794:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de una función.:@0.638498:0.654699:0.739551:0.654699:0.739551:0.639636:0.638498:0.639636:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Responde:@0.638503:0.798412:0.707456:0.798412:0.707456:0.782940:0.638503:0.782940:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
: ¿cómo se puede :@0.707456:0.797989:0.823267:0.797989:0.823267:0.782926:0.707456:0.782926:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
interpretar geométricamente y :@0.638503:0.813831:0.841526:0.813831:0.841526:0.798768:0.638503:0.798768:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
físicamente la derivada de una :@0.638503:0.829673:0.838219:0.829673:0.838219:0.814610:0.638503:0.814610:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
función?:@0.638503:0.845515:0.693912:0.845515:0.693912:0.830452:0.638503:0.830452:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Shutterstock, 377986132:@0.871305:0.774428:0.871305:0.706255:0.859836:0.706255:0.859836:0.774428:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Competencia :@0.685338:0.104916:0.782961:0.104916:0.782961:0.089444:0.685338:0.089444:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemática:@0.685338:0.117484:0.769401:0.117484:0.769401:0.102012:0.685338:0.102012:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Uno de los temas de :@0.685576:0.141959:0.822512:0.141959:0.822512:0.126896:0.685576:0.126896:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
interés del cálculo diferencial :@0.639033:0.157801:0.827684:0.157801:0.827684:0.142738:0.639033:0.142738:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de funciones reales de una sola :@0.639033:0.173643:0.842667:0.173643:0.842667:0.158580:0.639033:0.158580:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
variable es el análisis de la varia-:@0.639033:0.189485:0.840788:0.189485:0.840788:0.174422:0.639033:0.174422:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ción de la función. Esto significa :@0.639033:0.205327:0.847719:0.205327:0.847719:0.190264:0.639033:0.190264:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
que con cada función se debe :@0.639033:0.221169:0.836583:0.221169:0.836583:0.206106:0.639033:0.206106:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
realizar el estudio de la determi-:@0.639033:0.237011:0.843883:0.237011:0.843883:0.221948:0.639033:0.221948:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
nación de los subconjuntos del :@0.639033:0.252853:0.843603:0.252853:0.843603:0.237790:0.639033:0.237790:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
conjunto de salida, en los que :@0.639033:0.268695:0.834421:0.268695:0.834421:0.253632:0.639033:0.253632:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la función es creciente, decre-:@0.639033:0.284537:0.829969:0.284537:0.829969:0.269474:0.639033:0.269474:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ciente, así como los valores :@0.639033:0.300379:0.816532:0.300379:0.816532:0.285316:0.639033:0.285316:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
extremos de la función, es decir, :@0.639033:0.316221:0.847365:0.316221:0.847365:0.301158:0.639033:0.301158:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la existencia de los máximos o :@0.639033:0.332063:0.836741:0.332063:0.836741:0.317000:0.639033:0.317000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
mínimos locales, máximos o :@0.639033:0.347905:0.825503:0.347905:0.825503:0.332842:0.639033:0.332842:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
mínimos globales, paridad de :@0.639033:0.363747:0.831904:0.363747:0.831904:0.348684:0.639033:0.348684:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la función, e intersección de la :@0.639033:0.379589:0.836864:0.379589:0.836864:0.364526:0.639033:0.364526:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
gráfica de la función con los ejes :@0.639033:0.395431:0.850831:0.395431:0.850831:0.380367:0.639033:0.380367:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
coordenados.:@0.639033:0.411273:0.726524:0.411273:0.726524:0.396209:0.639033:0.396209:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 ©:@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