171:@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
Ejemplo 1:@0.073089:0.136836:0.148872:0.136836:0.148872:0.120167:0.073089:0.120167:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Consideremos las funciones: :@0.073089:0.160625:0.283138:0.160625:0.283138:0.144191:0.073089:0.144191:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a.    ( ) =  + 1 definida en [ 1,2];:@0.104633:0.184415:0.350217:0.184415:0.350217:0.167982:0.104633:0.167982:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.138792:0.184415:0.155671:0.184415:0.155671:0.168009:0.138792:0.168009:0.000000:0.000000:0.000000
x:@0.179177:0.184415:0.186632:0.184415:0.186632:0.168009:0.179177:0.168009:0.000000
3 :@0.186575:0.178352:0.194119:0.178352:0.194119:0.168771:0.186575:0.168771:0.000000:0.000000
–:@0.312151:0.184998:0.321355:0.184998:0.321355:0.167344:0.312151:0.167344:0.000000
b.    ( ) =  + 1 definida en ( 1,2) y :@0.104633:0.209276:0.363102:0.209276:0.363102:0.192842:0.104633:0.192842:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.138792:0.209276:0.155671:0.209276:0.155671:0.192870:0.138792:0.192870:0.000000:0.000000:0.000000
x:@0.179177:0.209276:0.186632:0.209276:0.186632:0.192870:0.179177:0.192870:0.000000
3 :@0.186575:0.203212:0.194119:0.203212:0.194119:0.193631:0.186575:0.193631:0.000000:0.000000
–:@0.312151:0.209859:0.321355:0.209859:0.321355:0.192204:0.312151:0.192204:0.000000
c.    ( ) =          si 0 ≤  < 3:@0.104633:0.234138:0.294848:0.234138:0.294848:0.217704:0.104633:0.217704:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.138792:0.234138:0.155671:0.234138:0.155671:0.217732:0.138792:0.217732:0.000000:0.000000:0.000000
x:@0.187092:0.234138:0.194547:0.234138:0.194547:0.217732:0.187092:0.217732:0.000000
x :@0.260371:0.234138:0.271066:0.234138:0.271066:0.217732:0.260371:0.217732:0.000000:0.000000
            :@0.134760:0.250780:0.182325:0.250780:0.182325:0.234346:0.134760:0.234346:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x :@0.182159:0.250780:0.192854:0.250780:0.192854:0.234374:0.182159:0.234374:0.000000:0.000000
– :@0.192798:0.251362:0.206512:0.251362:0.206512:0.233708:0.192798:0.233708:0.000000:0.000000
3 si 3 ≤   ≤ 4)      :@0.206512:0.250780:0.325631:0.250780:0.325631:0.234346:0.206512:0.234346:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.261476:0.250780:0.268931:0.250780:0.268931:0.234374:0.261476:0.234374:0.000000
d.    ( ) =    1 definida en (0,1].:@0.104633:0.279013:0.342935:0.279013:0.342935:0.262579:0.104633:0.262579:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.138792:0.279013:0.155671:0.279013:0.155671:0.262607:0.138792:0.262607:0.000000:0.000000:0.000000
1:@0.183928:0.272175:0.192911:0.272175:0.192911:0.255741:0.183928:0.255741:0.000000
x:@0.182105:0.288567:0.189560:0.288567:0.189560:0.272161:0.182105:0.272161:0.000000
2:@0.189495:0.282500:0.194732:0.282500:0.194732:0.272920:0.189495:0.272920:0.000000
–:@0.201530:0.279595:0.210734:0.279595:0.210734:0.261941:0.201530:0.261941:0.000000
Y analicemos sobre sus gráficas si tienen o no valores extremos.:@0.073103:0.327815:0.531603:0.327815:0.531603:0.311381:0.073103:0.311381:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Figura 2.2 :@0.073089:0.354550:0.133521:0.354550:0.133521:0.341105:0.073089:0.341105:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Figura 2.3:@0.310714:0.354550:0.367913:0.354550:0.367913:0.341105:0.310714:0.341105:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.632354:0.142228:0.637224:0.142228:0.637224:0.132218:0.632354:0.132218:0.000000
x:@0.724056:0.204003:0.728927:0.204003:0.728927:0.193993:0.724056:0.193993:0.000000
0:@0.640926:0.199623:0.645562:0.199623:0.645562:0.191439:0.640926:0.191439:0.000000
5:@0.641649:0.143198:0.646285:0.143198:0.646285:0.135014:0.641649:0.135014:0.000000
f(x)  :@0.674546:0.149270:0.699750:0.149270:0.699750:0.139260:0.674546:0.139260:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 =:@0.688816:0.149270:0.697740:0.149270:0.697740:0.139268:0.688816:0.139268:0.000000:0.000000
{:@0.700173:0.153688:0.705069:0.153688:0.705069:0.134390:0.700173:0.134390:0.000000
x:@0.707018:0.144757:0.711889:0.144757:0.711889:0.134747:0.707018:0.134747:0.000000
si:@0.728754:0.144757:0.735403:0.144757:0.735403:0.134747:0.728754:0.134747:0.000000:0.000000
 0 ≤   <3 :@0.735403:0.144757:0.776477:0.144757:0.776477:0.134756:0.735403:0.134756:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.754675:0.144757:0.759546:0.144757:0.759546:0.134747:0.754675:0.134747:0.000000
x:@0.707018:0.153078:0.711889:0.153078:0.711889:0.143068:0.707018:0.143068:0.000000
 - 3   3 ≤   ≤ 4 :@0.711889:0.153078:0.778035:0.153078:0.778035:0.143077:0.711889:0.143077:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
si:@0.727970:0.153078:0.734619:0.153078:0.734619:0.143068:0.727970:0.143068:0.000000:0.000000
x:@0.753891:0.153078:0.758762:0.153078:0.758762:0.143068:0.753891:0.143068:0.000000
f :@0.598032:0.244828:0.605966:0.244828:0.605966:0.228422:0.598032:0.228422:0.000000:0.000000
es continua:@0.605906:0.244828:0.690395:0.244828:0.690395:0.228394:0.605906:0.228394:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Valor máximo: no hay:@0.598027:0.261470:0.754161:0.261470:0.754161:0.245036:0.598027:0.245036:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Valor mínimo:  1:@0.598027:0.278112:0.720104:0.278112:0.720104:0.261678:0.598027:0.261678:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
–:@0.702010:0.278694:0.711214:0.278694:0.711214:0.261040:0.702010:0.261040:0.000000
Figura 2.5:@0.598032:0.313034:0.655226:0.313034:0.655226:0.299588:0.598032:0.299588:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.636974:0.342516:0.642829:0.342516:0.642829:0.330481:0.636974:0.330481:0.000000
x:@0.744897:0.443359:0.750753:0.443359:0.750753:0.431324:0.744897:0.431324:0.000000
0:@0.648672:0.436688:0.654246:0.436688:0.654246:0.426849:0.648672:0.426849:0.000000
10:@0.643099:0.393699:0.654246:0.393699:0.654246:0.383860:0.643099:0.383860:0.000000:0.000000
20:@0.643099:0.355252:0.654246:0.355252:0.654246:0.345413:0.643099:0.345413:0.000000:0.000000
2:@0.720580:0.436696:0.726153:0.436696:0.726153:0.426857:0.720580:0.426857:0.000000
f(x)  :@0.678767:0.345396:0.709067:0.345396:0.709067:0.333361:0.678767:0.333361:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 =:@0.695922:0.345396:0.706650:0.345396:0.706650:0.333371:0.695922:0.333371:0.000000:0.000000
 :@0.709067:0.342213:0.711370:0.342213:0.711370:0.332374:0.709067:0.332374:0.000000
x:@0.711224:0.352195:0.717079:0.352195:0.717079:0.340160:0.711224:0.340160:0.000000
2:@0.717081:0.349012:0.722654:0.349012:0.722654:0.339173:0.717081:0.339173:0.000000
- 1 :@0.724852:0.345483:0.741370:0.345483:0.741370:0.333458:0.724852:0.333458:0.000000:0.000000:0.000000:0.000000
1:@0.711614:0.340771:0.718425:0.340771:0.718425:0.328746:0.711614:0.328746:0.000000
denida en -1,2:@0.675463:0.363513:0.768555:0.363513:0.768555:0.351488:0.675463:0.351488:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f :@0.598032:0.489097:0.605966:0.489097:0.605966:0.472691:0.598032:0.472691:0.000000:0.000000
es continua:@0.605906:0.489097:0.690395:0.489097:0.690395:0.472663:0.605906:0.472663:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Valor máximo: no hay:@0.598027:0.505739:0.754161:0.505739:0.754161:0.489305:0.598027:0.489305:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Valor mínimo: no hay:@0.598027:0.522381:0.751621:0.522381:0.751621:0.505947:0.598027:0.505947:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2.1 Teorema de existencia de valores extremos:@0.073089:0.615728:0.436883:0.615728:0.436883:0.598781:0.073089:0.598781:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Si   es continua en un intervalo cerrado [ ,  ], entonces   tiene un :@0.073089:0.643090:0.557798:0.643090:0.557798:0.626656:0.073089:0.626656:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.089987:0.643090:0.094681:0.643090:0.094681:0.626684:0.089987:0.626684:0.000000
a b:@0.371729:0.643090:0.397959:0.643090:0.397959:0.626684:0.371729:0.626684:0.000000:0.000000:0.000000
f:@0.483140:0.643090:0.487834:0.643090:0.487834:0.626684:0.483140:0.626684:0.000000
valor máximo  ( ) y un valor mínimo  ( ) en ese intervalo en los :@0.073089:0.659731:0.557889:0.659731:0.557889:0.643298:0.073089:0.643298:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f c:@0.181066:0.659731:0.198553:0.659731:0.198553:0.643325:0.181066:0.643325:0.000000:0.000000:0.000000
f d:@0.353137:0.659731:0.372226:0.659731:0.372226:0.643325:0.353137:0.643325:0.000000:0.000000:0.000000
números  , :@0.073089:0.676373:0.156750:0.676373:0.156750:0.659939:0.073089:0.659939:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
c d :@0.142006:0.676373:0.169157:0.676373:0.169157:0.659967:0.142006:0.659967:0.000000:0.000000:0.000000:0.000000
[:@0.169102:0.676235:0.184435:0.676235:0.184435:0.662186:0.169102:0.662186:0.000000
 :@0.184343:0.676956:0.188945:0.676956:0.188945:0.659302:0.184343:0.659302:0.000000
[ ,  ].:@0.188853:0.676373:0.227103:0.676373:0.227103:0.659939:0.188853:0.659939:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a b:@0.193657:0.676373:0.219169:0.676373:0.219169:0.659967:0.193657:0.659967:0.000000:0.000000:0.000000
En las gráficas del Ejemplo 1 pudimos observar que los extremos se :@0.073071:0.703735:0.557843:0.703735:0.557843:0.687301:0.073071:0.687301:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
presentaron en puntos terminales (extremos del intervalo), pero no :@0.073071:0.720377:0.557990:0.720377:0.557990:0.703943:0.073071:0.703943:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
siempre es así. Algunas veces ocurren en puntos interiores del :@0.073071:0.737019:0.557690:0.737019:0.557690:0.720585:0.073071:0.720585:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
intervalo, como se puede observar en la gráfica de la función :@0.073071:0.753661:0.557795:0.753661:0.557795:0.737227:0.073071:0.737227:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y x:@0.073071:0.770303:0.098823:0.770303:0.098823:0.753897:0.073071:0.753897:0.000000:0.000000:0.000000
= +3 +2 dada a continuación (Figura 2.6).:@0.080471:0.770303:0.395575:0.770298:0.395575:0.753864:0.080471:0.753869:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3:@0.098775:0.764234:0.104012:0.764234:0.104012:0.754653:0.098775:0.754653:0.000000
x:@0.123752:0.770298:0.131207:0.770298:0.131207:0.753891:0.123752:0.753891:0.000000
2:@0.131145:0.764234:0.136382:0.764234:0.136382:0.754653:0.131145:0.754653:0.000000
Figura 2.6:@0.599612:0.595435:0.656806:0.595435:0.656806:0.581989:0.599612:0.581989:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y = x:@0.827618:0.620698:0.851969:0.620698:0.851969:0.608715:0.827618:0.608715:0.000000:0.000000:0.000000:0.000000:0.000000
3 :@0.851969:0.617528:0.859811:0.617528:0.859811:0.607732:0.851969:0.607732:0.000000:0.000000
+ 3:@0.859810:0.620698:0.877274:0.620698:0.877274:0.608725:0.859810:0.608725:0.000000:0.000000:0.000000
x:@0.877274:0.620698:0.883104:0.620698:0.883104:0.608715:0.877274:0.608715:0.000000
2 :@0.883104:0.617528:0.890946:0.617528:0.890946:0.607732:0.883104:0.607732:0.000000:0.000000
+ 2 :@0.890945:0.620698:0.911212:0.620698:0.911212:0.608725:0.890945:0.608725:0.000000:0.000000:0.000000:0.000000
Máximo relativo:@0.620096:0.679908:0.692696:0.679908:0.692696:0.669950:0.620096:0.669950:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Mínimo relativo:@0.708629:0.696509:0.779346:0.696509:0.779346:0.686551:0.708629:0.686551:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(-2,6):@0.639052:0.696202:0.669454:0.696202:0.669454:0.683141:0.639052:0.683141:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(0,2):@0.729800:0.712502:0.755774:0.712502:0.755774:0.699441:0.729800:0.699441:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.835461:0.745177:0.841291:0.745177:0.841291:0.733195:0.835461:0.733195:0.000000
y:@0.725602:0.628178:0.731432:0.628178:0.731432:0.616195:0.725602:0.616195:0.000000
0:@0.736045:0.737030:0.741594:0.737030:0.741594:0.727234:0.736045:0.727234:0.000000
2:@0.809759:0.737030:0.815308:0.737030:0.815308:0.727234:0.809759:0.727234:0.000000
-2:@0.670692:0.737030:0.679562:0.737030:0.679562:0.727234:0.670692:0.727234:0.000000:0.000000
-1:@0.603392:0.737030:0.612262:0.737030:0.612262:0.727234:0.603392:0.727234:0.000000:0.000000
-10:@0.726808:0.775970:0.741226:0.775970:0.741226:0.766174:0.726808:0.766174:0.000000:0.000000:0.000000
10:@0.730507:0.687285:0.741605:0.687285:0.741605:0.677489:0.730507:0.677489:0.000000:0.000000
20:@0.730507:0.643268:0.741605:0.643268:0.741605:0.633472:0.730507:0.633472:0.000000:0.000000
f(x)  x:@0.166789:0.402307:0.196438:0.402307:0.196438:0.392439:0.166789:0.392439:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 =:@0.180857:0.402307:0.189654:0.402307:0.189654:0.392447:0.180857:0.392447:0.000000:0.000000
3:@0.196436:0.399698:0.200819:0.399698:0.200819:0.391623:0.196436:0.391623:0.000000
 :@0.200819:0.399698:0.202708:0.399698:0.202708:0.391630:0.200819:0.391630:0.000000
+ 1 :@0.202708:0.402307:0.219400:0.402307:0.219400:0.392447:0.202708:0.392447:0.000000:0.000000:0.000000:0.000000
denida en -1,2:@0.165242:0.413496:0.241579:0.413496:0.241579:0.403636:0.165242:0.403636:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.106925:0.399346:0.111726:0.399346:0.111726:0.389477:0.106925:0.389477:0.000000
x:@0.204592:0.430666:0.209394:0.430666:0.209394:0.420797:0.204592:0.420797:0.000000
0:@0.118017:0.425603:0.122587:0.425603:0.122587:0.417536:0.118017:0.417536:0.000000
2:@0.181838:0.425355:0.186408:0.425355:0.186408:0.417288:0.181838:0.417288:0.000000
            :@0.252763:0.456781:0.300327:0.456781:0.300327:0.440347:0.252763:0.440347:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.335508:0.400204:0.340523:0.400204:0.340523:0.389899:0.335508:0.389899:0.000000
x:@0.437513:0.432909:0.442528:0.432909:0.442528:0.422604:0.437513:0.422604:0.000000
0:@0.347093:0.427620:0.351866:0.427620:0.351866:0.419196:0.347093:0.419196:0.000000
2:@0.413750:0.427361:0.418523:0.427361:0.418523:0.418937:0.413750:0.418937:0.000000
f(x)  x:@0.398031:0.403295:0.428996:0.403295:0.428996:0.392991:0.398031:0.392991:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 =:@0.412723:0.403295:0.421912:0.403295:0.421912:0.392999:0.412723:0.392999:0.000000:0.000000
3:@0.428995:0.400570:0.433573:0.400570:0.433573:0.392139:0.428995:0.392139:0.000000
 :@0.433573:0.400570:0.435546:0.400570:0.435546:0.392146:0.433573:0.392146:0.000000
+ 1 :@0.435545:0.403295:0.452978:0.403295:0.452978:0.392999:0.435545:0.392999:0.000000:0.000000:0.000000:0.000000
denida en (-1,2):@0.396414:0.414979:0.476142:0.414979:0.476142:0.404683:0.396414:0.404683:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.073089:0.484144:0.077783:0.484144:0.077783:0.467738:0.073089:0.467738:0.000000
 es continua :@0.077716:0.484144:0.170121:0.484144:0.170121:0.467710:0.077716:0.467710:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f :@0.309037:0.484144:0.316970:0.484144:0.316970:0.467738:0.309037:0.467738:0.000000:0.000000
es continua:@0.316915:0.484144:0.401404:0.484144:0.401404:0.467710:0.316915:0.467710:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Valor máximo: 1 :@0.073089:0.500786:0.192638:0.500786:0.192638:0.484352:0.073089:0.484352:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Valor máximo: no hay:@0.309034:0.500786:0.465175:0.500786:0.465175:0.484352:0.309034:0.484352:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Valor mínimo:  1 :@0.073089:0.517427:0.199117:0.517427:0.199117:0.500994:0.073089:0.500994:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
–:@0.177071:0.518010:0.186275:0.518010:0.186275:0.500356:0.177071:0.500356:0.000000
Valor mínimo: no hay:@0.309027:0.517427:0.462628:0.517427:0.462628:0.500994:0.309027:0.500994:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.073089:0.547055:0.076387:0.547055:0.076387:0.533609:0.073089:0.533609:0.000000
Definición 2::@0.114199:0.813469:0.209103:0.813469:0.209103:0.796800:0.114199:0.796800:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sea la función definida en un intervalo :@0.114199:0.840831:0.396581:0.840831:0.396581:0.824397:0.114199:0.824397:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
D; c:@0.396253:0.840831:0.422049:0.840831:0.422049:0.824425:0.396253:0.824425:0.000000:0.000000:0.000000:0.000000
    .:@0.422005:0.840831:0.459813:0.840831:0.459813:0.824397:0.422005:0.824397:0.000000:0.000000:0.000000:0.000000:0.000000
[:@0.425962:0.840693:0.441296:0.840693:0.441296:0.826644:0.425962:0.826644:0.000000
D:@0.445161:0.840831:0.456684:0.840831:0.456684:0.824425:0.445161:0.824425:0.000000
a.  Si existe algún intervalo abierto en el que  ( ) es el valor máximo, se concluye que  ( ) es un :@0.145743:0.868196:0.855078:0.868196:0.855078:0.851762:0.145743:0.851762:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f c:@0.486751:0.868196:0.504017:0.868196:0.504017:0.851790:0.486751:0.851790:0.000000:0.000000:0.000000
f c:@0.784285:0.868196:0.801551:0.868196:0.801551:0.851790:0.784285:0.851790:0.000000:0.000000:0.000000
máximo relativo de  .:@0.175889:0.884837:0.327196:0.884837:0.327196:0.868404:0.175889:0.868404:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.319373:0.884837:0.324067:0.884837:0.324067:0.868431:0.319373:0.868431:0.000000
b.  Si existe algún intervalo abierto en el que  ( ) es el valor mínimo, se concluye que  ( ) es un :@0.145743:0.909699:0.855024:0.909699:0.855024:0.893265:0.145743:0.893265:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f c:@0.487910:0.909699:0.505195:0.909699:0.505195:0.893293:0.487910:0.893293:0.000000:0.000000:0.000000
f c:@0.783991:0.909699:0.801275:0.909699:0.801275:0.893293:0.783991:0.893293:0.000000:0.000000:0.000000
mínimo relativo de  .:@0.175834:0.926341:0.324601:0.926341:0.324601:0.909907:0.175834:0.909907:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.316778:0.926341:0.321472:0.926341:0.321472:0.909935:0.316778:0.909935:0.000000
Figura 2.4:@0.811488:0.216512:0.868682:0.216512:0.868682:0.203066:0.811488:0.203066:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
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