177:@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
3.1 Funciones crecientes y decrecientes:@0.073089:0.248814:0.381026:0.248814:0.381026:0.231867:0.073089:0.231867:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Una función:@0.096806:0.283325:0.187462:0.283325:0.187462:0.266891:0.096806:0.266891:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 es creciente:@0.187499:0.283325:0.283461:0.283325:0.283461:0.266655:0.187499:0.266655:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 en un intervalo   si para todo  ,       con   <   se :@0.283492:0.283325:0.686657:0.283325:0.686657:0.266891:0.283492:0.266891:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
D:@0.405036:0.283325:0.416558:0.283325:0.416558:0.266919:0.405036:0.266919:0.000000
x x:@0.513233:0.283325:0.540485:0.283325:0.540485:0.266919:0.513233:0.266919:0.000000:0.000000:0.000000
1:@0.520710:0.283071:0.525233:0.283071:0.525233:0.274796:0.520710:0.274796:0.000000
2:@0.540503:0.283071:0.545026:0.283071:0.545026:0.274796:0.540503:0.274796:0.000000
∈:@0.549601:0.283907:0.564935:0.283907:0.564935:0.266253:0.549601:0.266253:0.000000
D:@0.569518:0.283325:0.581041:0.283325:0.581041:0.266919:0.569518:0.266919:0.000000
x:@0.618113:0.283325:0.625568:0.283325:0.625568:0.266919:0.618113:0.266919:0.000000
1:@0.625590:0.283071:0.630113:0.283071:0.630113:0.274796:0.625590:0.274796:0.000000
x:@0.650242:0.283325:0.657697:0.283325:0.657697:0.266919:0.650242:0.266919:0.000000
2:@0.657712:0.283071:0.662235:0.283071:0.662235:0.274796:0.657712:0.274796:0.000000
cumple que  ( ) <  ( ).:@0.096811:0.299967:0.262898:0.299967:0.262898:0.283533:0.096811:0.283533:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.188719:0.299967:0.205598:0.299967:0.205598:0.283560:0.188719:0.283560:0.000000:0.000000:0.000000
1:@0.205525:0.299713:0.210047:0.299713:0.210047:0.291438:0.205525:0.291438:0.000000
f x:@0.233586:0.299967:0.250465:0.299967:0.250465:0.283560:0.233586:0.283560:0.000000:0.000000:0.000000
2:@0.250408:0.299713:0.254931:0.299713:0.254931:0.291438:0.250408:0.291438:0.000000
Una función :@0.096810:0.327328:0.189619:0.327328:0.189619:0.310895:0.096810:0.310895:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
es decreciente :@0.189104:0.327328:0.302054:0.327328:0.302054:0.310659:0.189104:0.310659:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
en un intervalo   si para todo  ,       con  , <   se :@0.301572:0.327328:0.686665:0.327330:0.686665:0.310896:0.301572:0.310895:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
D:@0.414298:0.327328:0.425821:0.327328:0.425821:0.310922:0.414298:0.310922:0.000000
x x:@0.517471:0.327328:0.543498:0.327330:0.543498:0.310924:0.517471:0.310922:0.000000:0.000000:0.000000
1:@0.524862:0.327076:0.529385:0.327076:0.529385:0.318801:0.524862:0.318801:0.000000
2 :@0.543442:0.327076:0.549957:0.327076:0.549957:0.318801:0.543442:0.318801:0.000000:0.000000
∈:@0.553318:0.327912:0.568651:0.327912:0.568651:0.310258:0.553318:0.310258:0.000000
D:@0.572148:0.327330:0.583671:0.327330:0.583671:0.310924:0.572148:0.310924:0.000000
x:@0.618406:0.327330:0.625861:0.327330:0.625861:0.310924:0.618406:0.310924:0.000000
1:@0.625787:0.327076:0.630310:0.327076:0.630310:0.318801:0.625787:0.318801:0.000000
x:@0.651455:0.327330:0.658910:0.327330:0.658910:0.310924:0.651455:0.310924:0.000000
2:@0.658842:0.327076:0.663364:0.327076:0.663364:0.318801:0.658842:0.318801:0.000000
cumple que  ( ) >  ( ).:@0.096805:0.343972:0.262898:0.343972:0.262898:0.327538:0.096805:0.327538:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.188712:0.343972:0.205591:0.343972:0.205591:0.327566:0.188712:0.327566:0.000000:0.000000:0.000000
1:@0.205525:0.343718:0.210047:0.343718:0.210047:0.335443:0.205525:0.335443:0.000000
f x:@0.233586:0.343972:0.250465:0.343972:0.250465:0.327566:0.233586:0.327566:0.000000:0.000000:0.000000
2:@0.250408:0.343718:0.254931:0.343718:0.254931:0.335443:0.250408:0.335443:0.000000
Ejemplo 1.:@0.073083:0.387060:0.155234:0.387060:0.155234:0.370390:0.073083:0.370390:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.155381:0.387060:0.159413:0.387060:0.159413:0.370626:0.155381:0.370626:0.000000
Determinemos en qué intervalos abiertos la función dada es creciente o :@0.160536:0.387060:0.710377:0.387060:0.710377:0.370626:0.160536:0.370626:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.553899:0.387060:0.557930:0.387060:0.557930:0.370626:0.553899:0.370626:0.000000
decreciente.:@0.073083:0.403702:0.161933:0.403702:0.161933:0.387268:0.073083:0.387268:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Con ayuda de una calculadora gráfica podemos obtener la gráfica de la función y :@0.073089:0.482304:0.710297:0.482304:0.710297:0.465870:0.073089:0.465870:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
observar en qué intervalo la función crece, decrece o es constante.:@0.073074:0.498946:0.555412:0.498946:0.555412:0.482512:0.073074:0.482512:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Figura 3.1:@0.361141:0.525678:0.418335:0.525678:0.418335:0.512232:0.361141:0.512232:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
0:@0.305382:0.708110:0.311169:0.708110:0.311169:0.697895:0.305382:0.697895:0.000000
10:@0.299144:0.642641:0.310718:0.642641:0.310718:0.632427:0.299144:0.632427:0.000000:0.000000
20:@0.299144:0.582840:0.310718:0.582840:0.310718:0.572626:0.299144:0.572626:0.000000:0.000000
2:@0.378708:0.708110:0.384496:0.708110:0.384496:0.697895:0.378708:0.697895:0.000000
4:@0.443258:0.708110:0.449045:0.708110:0.449045:0.697895:0.443258:0.697895:0.000000
6:@0.509060:0.708110:0.514847:0.708110:0.514847:0.697895:0.509060:0.697895:0.000000
-2:@0.243483:0.708110:0.252734:0.708110:0.252734:0.697895:0.243483:0.697895:0.000000:0.000000
y:@0.285290:0.559705:0.291370:0.559705:0.291370:0.547210:0.285290:0.547210:0.000000
x:@0.526812:0.717746:0.532892:0.717746:0.532892:0.705251:0.526812:0.705251:0.000000
(1,1):@0.334589:0.681821:0.361483:0.681821:0.361483:0.668201:0.334589:0.668201:0.000000:0.000000:0.000000:0.000000:0.000000
(3,1):@0.397927:0.681821:0.424821:0.681821:0.424821:0.668201:0.397927:0.668201:0.000000:0.000000:0.000000:0.000000:0.000000
Constante:@0.353271:0.691192:0.402986:0.691192:0.402986:0.680808:0.353271:0.680808:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Decreciente:@0.246658:0.623810:0.265990:0.664991:0.278987:0.661528:0.259655:0.620348:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f(x) = :@0.401098:0.566142:0.432149:0.566142:0.432149:0.553647:0.401098:0.553647:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
-( -1) +1:@0.444337:0.556493:0.497260:0.556497:0.497260:0.544013:0.444337:0.544008:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.452486:0.556493:0.458566:0.556493:0.458566:0.543998:0.452486:0.543998:0.000000
3 :@0.473792:0.553192:0.481971:0.553192:0.481971:0.542978:0.473792:0.542978:0.000000:0.000000
x:@0.514550:0.556497:0.520631:0.556497:0.520631:0.544002:0.514550:0.544002:0.000000
<1:@0.520631:0.556497:0.535922:0.556497:0.535922:0.544013:0.520631:0.544013:0.000000:0.000000
-( -3) +1:@0.444343:0.576606:0.497260:0.576608:0.497260:0.564123:0.444343:0.564121:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.452491:0.576606:0.458572:0.576606:0.458572:0.564111:0.452491:0.564111:0.000000
2 :@0.473792:0.573302:0.481971:0.573302:0.481971:0.563088:0.473792:0.563088:0.000000:0.000000
x:@0.514550:0.576608:0.520631:0.576608:0.520631:0.564113:0.514550:0.564113:0.000000
>3:@0.520631:0.576608:0.535922:0.576608:0.535922:0.564123:0.520631:0.564123:0.000000:0.000000
1≤   ≤ 3:@0.490477:0.566356:0.535908:0.566356:0.535908:0.553871:0.490477:0.553871:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.508691:0.566356:0.514771:0.566356:0.514771:0.553861:0.508691:0.553861:0.000000
1:@0.447886:0.566356:0.454959:0.566356:0.454959:0.553871:0.447886:0.553871:0.000000
{:@0.433697:0.580937:0.441719:0.580937:0.441719:0.536355:0.433697:0.536355:0.000000
Creciente:@0.515404:0.658772:0.541075:0.629912:0.529623:0.624131:0.503952:0.652991:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
De la gráfica mostrada en la Figura 3.1 podemos concluir que   decrece en (:@0.073089:0.764439:0.642997:0.764439:0.642997:0.748005:0.073089:0.748005:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.540319:0.764439:0.545013:0.764439:0.545013:0.748033:0.540319:0.748033:0.000000
–:@0.643124:0.765021:0.652327:0.765021:0.652327:0.747367:0.643124:0.747367:0.000000
`:@0.652438:0.763884:0.664715:0.763884:0.664715:0.750168:0.652438:0.750168:0.000000
,1), es :@0.664826:0.764439:0.710365:0.764439:0.710365:0.748005:0.664826:0.748005:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
constante en (1,3) y crece en (3,  ).:@0.073088:0.781081:0.325083:0.781081:0.325083:0.764647:0.073088:0.764647:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
`:@0.304890:0.780526:0.317168:0.780526:0.317168:0.766810:0.304890:0.766810:0.000000
A continuación, conoceremos varios criterios que nos facilitan la determinación de :@0.073088:0.808443:0.709881:0.808443:0.709881:0.792009:0.073088:0.792009:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
dónde una función crece o decrece y dónde presenta valores extremos.:@0.073088:0.825084:0.592485:0.825084:0.592485:0.808651:0.073088:0.808651:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Tema 3. Monotonía y concavidad:@0.073089:0.098522:0.559807:0.098522:0.559807:0.067281:0.073089:0.067281:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
observa las gráficas de las funciones lineales en el cuadro de la derecha y determina :@0.101550:0.172733:0.710914:0.172733:0.710914:0.156300:0.101550:0.156300:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cuáles son crecientes y cuáles decrecientes:  :@0.101550:0.189377:0.424321:0.189377:0.424321:0.172943:0.101550:0.172943:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿La función sube (creciente) o baja (decreciente) al moverse en esa dirección?:@0.101550:0.206018:0.663313:0.206018:0.663313:0.189585:0.101550:0.189585:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Reto matemático:@0.110658:0.139600:0.245381:0.139600:0.245381:0.122653:0.110658:0.122653:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Criterios para determinar si una función es creciente decreciente:@0.128825:0.862311:0.615507:0.862311:0.615507:0.845641:0.128825:0.845641:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Si   es una función derivable en una intervalo ( ,  )::@0.128825:0.884319:0.495994:0.884319:0.495994:0.867886:0.128825:0.867886:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.145004:0.884319:0.149698:0.884319:0.149698:0.867913:0.145004:0.867913:0.000000
a b:@0.462548:0.884319:0.488060:0.884319:0.488060:0.867913:0.462548:0.867913:0.000000:0.000000:0.000000
Si  ´( ) > 0 sobre un intervalo, entonces   es creciente en ese intervalo.:@0.128788:0.906328:0.633793:0.906328:0.633793:0.889894:0.128788:0.889894:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f  x:@0.144968:0.906328:0.170535:0.906328:0.170535:0.889922:0.144968:0.889922:0.000000:0.000000:0.000000:0.000000
f:@0.416788:0.906328:0.421481:0.906328:0.421481:0.889922:0.416788:0.889922:0.000000
Si   ´( ) < 0 sobre un intervalo, entonces   es decreciente en ese intervalo.:@0.128788:0.928337:0.641071:0.928337:0.641071:0.911903:0.128788:0.911903:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.144305:0.928337:0.169854:0.928337:0.169854:0.911931:0.144305:0.911931:0.000000:0.000000:0.000000
f:@0.410253:0.928337:0.414947:0.928337:0.414947:0.911931:0.410253:0.911931:0.000000
30:@0.745493:0.616666:0.750846:0.616666:0.750846:0.611770:0.745493:0.611770:0.000000:0.000000
20:@0.745493:0.629752:0.750846:0.629752:0.750846:0.624856:0.745493:0.624856:0.000000:0.000000
10:@0.745493:0.642838:0.750846:0.642838:0.750846:0.637942:0.745493:0.637942:0.000000:0.000000
0:@0.748169:0.655924:0.750846:0.655924:0.750846:0.651028:0.748169:0.651028:0.000000
-10:@0.743859:0.669010:0.750846:0.669010:0.750846:0.664113:0.743859:0.664113:0.000000:0.000000:0.000000
-20:@0.743859:0.682096:0.750846:0.682096:0.750846:0.677199:0.743859:0.677199:0.000000:0.000000:0.000000
-10.0:@0.755732:0.695326:0.766350:0.695326:0.766350:0.690430:0.755732:0.690430:0.000000:0.000000:0.000000:0.000000:0.000000
 10.0:@0.909486:0.695326:0.919671:0.695326:0.919671:0.690430:0.909486:0.690430:0.000000:0.000000:0.000000:0.000000:0.000000
-7.5:@0.775937:0.695326:0.783878:0.695326:0.783878:0.690430:0.775937:0.690430:0.000000:0.000000:0.000000:0.000000
7.5:@0.892337:0.695326:0.898644:0.695326:0.898644:0.690430:0.892337:0.690430:0.000000:0.000000:0.000000
-5.0:@0.795017:0.695326:0.802958:0.695326:0.802958:0.690430:0.795017:0.690430:0.000000:0.000000:0.000000:0.000000
5.0:@0.872818:0.695326:0.879125:0.695326:0.879125:0.690430:0.872818:0.690430:0.000000:0.000000:0.000000
-2.5:@0.814536:0.695326:0.822477:0.695326:0.822477:0.690430:0.814536:0.690430:0.000000:0.000000:0.000000:0.000000
2.5:@0.853518:0.695326:0.859825:0.695326:0.859825:0.690430:0.853518:0.690430:0.000000:0.000000:0.000000
0.0:@0.834652:0.695326:0.840959:0.695326:0.840959:0.690430:0.834652:0.690430:0.000000:0.000000:0.000000
x:@0.836764:0.699954:0.839116:0.699954:0.839116:0.695058:0.836764:0.695058:0.000000
f(x), g(x), h(x):@0.743460:0.657284:0.743460:0.636604:0.736961:0.636604:0.736961:0.657284:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f  x:@0.805022:0.159713:0.824494:0.159713:0.824494:0.144744:0.805022:0.144744:0.000000:0.000000:0.000000:0.000000
( ) = 2  + 1:@0.812586:0.159713:0.886429:0.159713:0.886429:0.144756:0.812586:0.144756:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.854091:0.159713:0.861375:0.159713:0.861375:0.144744:0.854091:0.144744:0.000000
g( ) = – 3  + 5:@0.805022:0.174645:0.899642:0.174645:0.899642:0.159688:0.805022:0.159688:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.818813:0.174645:0.826096:0.174645:0.826096:0.159676:0.818813:0.159676:0.000000
x:@0.867304:0.174645:0.874587:0.174645:0.874587:0.159676:0.867304:0.159676:0.000000
h( ) = 0,5  – 2:@0.805022:0.189577:0.898123:0.189577:0.898123:0.174620:0.805022:0.174620:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.818747:0.189577:0.826030:0.189577:0.826030:0.174608:0.818747:0.174608:0.000000
x:@0.867370:0.189577:0.874653:0.189577:0.874653:0.174608:0.867370:0.174608:0.000000
Observar el signo :@0.740294:0.323198:0.858806:0.323198:0.858806:0.308258:0.740294:0.308258:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de la pendiente (o la :@0.740294:0.338327:0.879240:0.338327:0.879240:0.323387:0.740294:0.323387:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
derivada en funciones :@0.740294:0.353456:0.890089:0.353456:0.890089:0.338516:0.740294:0.338516:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
no lineales) te ayuda a :@0.740294:0.368585:0.890299:0.368585:0.890299:0.353645:0.740294:0.353645:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
identificar rápidamente :@0.740294:0.383714:0.898322:0.383714:0.898322:0.368774:0.740294:0.368774:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
el comportamiento de la :@0.740294:0.398843:0.908106:0.398843:0.908106:0.383903:0.740294:0.383903:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
función sin necesidad de :@0.740294:0.413972:0.908618:0.413972:0.908618:0.399032:0.740294:0.399032:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
graficarla, solo observando :@0.740294:0.429101:0.920767:0.429101:0.920767:0.414161:0.740294:0.414161:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
el signo de la pendiente o :@0.740294:0.444230:0.915302:0.444230:0.915302:0.429290:0.740294:0.429290:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
derivada en cada intervalo.::@0.740294:0.459359:0.920156:0.459359:0.920156:0.444419:0.740294:0.444419:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
•  Si el coeficiente de x :@0.740294:0.474488:0.897097:0.474488:0.897097:0.459548:0.740294:0.459548:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(en funciones lineales) :@0.759267:0.489617:0.909731:0.489617:0.909731:0.474677:0.759267:0.474677:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
o la derivada de la :@0.759267:0.504746:0.882421:0.504746:0.882421:0.489806:0.759267:0.489806:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
función es positiva en :@0.759267:0.519875:0.906742:0.519875:0.906742:0.504935:0.759267:0.504935:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
un intervalo, la función :@0.759267:0.535003:0.913752:0.535003:0.913752:0.520064:0.759267:0.520064:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
es creciente en ese :@0.759267:0.550132:0.888189:0.550132:0.888189:0.535193:0.759267:0.535193:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
intervalo.:@0.759267:0.565261:0.819959:0.565261:0.819959:0.550322:0.759267:0.550322:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
•  Si es negativa, la función :@0.740294:0.580390:0.924279:0.580390:0.924279:0.565450:0.740294:0.565450:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
es decreciente.:@0.759267:0.595519:0.857863:0.595519:0.857863:0.580579:0.759267:0.580579:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Competencia :@0.740290:0.281228:0.838982:0.281228:0.838982:0.265822:0.740290:0.265822:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemática :@0.740290:0.296357:0.828905:0.296357:0.828905:0.280951:0.740290:0.280951:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
MUESTRA EDITORIAL:@0.248902:0.947499:0.888171:0.113285:0.743922:0.050540:0.104653:0.884754:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 Muestra editorial solo para fines didácticos – Prohibida su venta:@0.095585:0.659700:0.095585:0.341447:0.077558:0.341447:0.077558:0.659700:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000