40:@0.036727:0.974518:0.057230:0.974518:0.057230:0.956333:0.036727:0.956333:0.000000:0.000000
Números reales y funciones:@0.073089:0.043661:0.318030:0.043661:0.318030:0.024916:0.073089:0.024916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Para elaborar la gráfica, haremos una tabla considerando algunos puntos de prueba que se obtienen al tomar un valor :@0.073089:0.136836:0.931520:0.136836:0.931520:0.121124:0.073089:0.121124:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.073089:0.153478:0.080544:0.153478:0.080544:0.138043:0.073089:0.138043:0.000000
 de cada uno de los intervalos determinados por los puntos de intersección en  .:@0.080470:0.153478:0.663354:0.153478:0.663354:0.137765:0.080470:0.137765:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.652770:0.153478:0.660225:0.153478:0.660225:0.138043:0.652770:0.138043:0.000000
x:@0.088004:0.196916:0.096122:0.196916:0.096122:0.180232:0.088004:0.180232:0.000000
2:@0.167450:0.196361:0.182783:0.196361:0.182783:0.182645:0.167450:0.182645:0.000000
6:@0.182691:0.196916:0.191674:0.196916:0.191674:0.181203:0.182691:0.181203:0.000000
2:@0.252841:0.196361:0.268174:0.196361:0.268174:0.182645:0.252841:0.182645:0.000000
5:@0.268082:0.196916:0.277065:0.196916:0.277065:0.181203:0.268082:0.181203:0.000000
2:@0.338232:0.196361:0.353565:0.196361:0.353565:0.182645:0.338232:0.182645:0.000000
3:@0.353473:0.196916:0.362456:0.196916:0.362456:0.181203:0.353473:0.181203:0.000000
2:@0.408014:0.196361:0.423347:0.196361:0.423347:0.182645:0.408014:0.182645:0.000000
1,861:@0.423255:0.196916:0.462095:0.196916:0.462095:0.181203:0.423255:0.181203:0.000000:0.000000:0.000000:0.000000:0.000000
0:@0.538466:0.196916:0.547449:0.196916:0.547449:0.181203:0.538466:0.181203:0.000000
3:@0.623857:0.196916:0.632840:0.196916:0.632840:0.181203:0.623857:0.181203:0.000000
5,19434:@0.680589:0.196916:0.737246:0.196916:0.737246:0.181203:0.680589:0.181203:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
7:@0.813599:0.196916:0.822582:0.196916:0.822582:0.181203:0.813599:0.181203:0.000000
8:@0.898972:0.196916:0.907955:0.196916:0.907955:0.181203:0.898972:0.181203:0.000000
y:@0.088022:0.232654:0.096140:0.232654:0.096140:0.215971:0.088022:0.215971:0.000000
2:@0.149668:0.232099:0.165001:0.232099:0.165001:0.218384:0.149668:0.218384:0.000000
117:@0.164909:0.232654:0.191710:0.232654:0.191710:0.216941:0.164909:0.216941:0.000000:0.000000:0.000000
0:@0.268100:0.232654:0.277083:0.232654:0.277083:0.216941:0.268100:0.216941:0.000000
120:@0.335674:0.232654:0.362474:0.232654:0.362474:0.216941:0.335674:0.216941:0.000000:0.000000:0.000000
135,20715:@0.387656:0.232654:0.462131:0.232654:0.462131:0.216941:0.387656:0.216941:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
105:@0.520666:0.232654:0.547467:0.232654:0.547467:0.216941:0.520666:0.216941:0.000000:0.000000:0.000000
0:@0.623857:0.232654:0.632840:0.232654:0.632840:0.216941:0.623857:0.216941:0.000000
2:@0.656549:0.232099:0.671882:0.232099:0.671882:0.218384:0.656549:0.218384:0.000000
40,39234:@0.671772:0.232654:0.737209:0.232654:0.737209:0.216941:0.671772:0.216941:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
0:@0.813581:0.232654:0.822564:0.232654:0.822564:0.216941:0.813581:0.216941:0.000000
65:@0.890063:0.232654:0.907955:0.232654:0.907955:0.216941:0.890063:0.216941:0.000000:0.000000
Después de graficar los pares ordenados de la tabla, se traza una curva continua para obtener un bosquejo de la gráfica. :@0.073094:0.272248:0.931341:0.272248:0.931341:0.256535:0.073094:0.256535:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Debemos también tener en cuenta el comportamiento de la gráfica de la funciones polinómicas estudiado en el :@0.073094:0.303895:0.930890:0.303895:0.930890:0.288182:0.073094:0.288182:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ejemplo 3. La otra alternativa es utilizar una calculadora gráfica, como por ejemplo Demos o GeoGebra.:@0.073094:0.320537:0.819131:0.320537:0.819131:0.304824:0.073094:0.304824:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Observemos que el :@0.073094:0.352184:0.223872:0.352184:0.223872:0.336471:0.073094:0.336471:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
máximo local:@0.224991:0.352184:0.329507:0.352184:0.329507:0.335515:0.224991:0.335515:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 se presenta cuando la función es creciente y luego decreciente en un entorno :@0.329673:0.352184:0.930992:0.352184:0.930992:0.336471:0.329673:0.336471:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
próximo de centro  1,861, y que el :@0.073094:0.368826:0.337713:0.368826:0.337713:0.353113:0.073094:0.353113:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.213873:0.368271:0.229206:0.368271:0.229206:0.354556:0.213873:0.354556:0.000000
mínimo local:@0.338085:0.368826:0.437493:0.368826:0.437493:0.352156:0.338085:0.352156:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 se presenta cuando la función es decreciente y luego creciente en :@0.437392:0.368826:0.930861:0.368826:0.930861:0.353113:0.437392:0.353113:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
un entorno próximo de centro 5,19434. En unidades posteriores se estudiarán estos conceptos con mayor formalidad.:@0.073094:0.385468:0.925690:0.385468:0.925690:0.369755:0.073094:0.369755:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A continuación, tenemos la gráfica de la función polinómica         5:@0.073094:0.417115:0.619542:0.417125:0.619542:0.401412:0.073094:0.401402:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.537417:0.417115:0.544890:0.417115:0.544890:0.401680:0.537417:0.401680:0.000000
5:@0.550413:0.416560:0.565746:0.416560:0.565746:0.402845:0.550413:0.402845:0.000000
x:@0.571323:0.417115:0.578778:0.417115:0.578778:0.401680:0.571323:0.401680:0.000000
3:@0.578924:0.411061:0.584161:0.411061:0.584161:0.401901:0.578924:0.401901:0.000000
2:@0.589649:0.416570:0.604982:0.416570:0.604982:0.402855:0.589649:0.402855:0.000000
x    :@0.619708:0.417125:0.655903:0.417125:0.655903:0.401690:0.619708:0.401690:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.627305:0.411061:0.632542:0.411061:0.632542:0.401901:0.627305:0.401901:0.000000
2:@0.637073:0.416570:0.652406:0.416570:0.652406:0.402855:0.637073:0.402855:0.000000
29:@0.657026:0.417125:0.675157:0.417125:0.675157:0.401412:0.657026:0.401412:0.000000:0.000000
x:@0.675304:0.417125:0.682759:0.417125:0.682759:0.401690:0.675304:0.401690:0.000000
 :@0.682907:0.411061:0.685257:0.411061:0.685257:0.401901:0.682907:0.401901:0.000000
1:@0.686056:0.416570:0.701389:0.416570:0.701389:0.402855:0.686056:0.402855:0.000000
 105 con todos los elementos :@0.701573:0.417125:0.930999:0.417125:0.930999:0.401412:0.701573:0.401412:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.734405:0.416810:0.738070:0.416810:0.738070:0.402526:0.734405:0.402526:0.000000
previamente trabajados. :@0.073083:0.433767:0.252745:0.433767:0.252745:0.418054:0.073083:0.418054:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
0:@0.433547:0.715957:0.441713:0.715957:0.441713:0.701673:0.433547:0.701673:0.000000
2:@0.339034:0.717445:0.352973:0.717445:0.352973:0.704976:0.339034:0.704976:0.000000
5:@0.352973:0.717949:0.361139:0.717949:0.361139:0.703665:0.352973:0.703665:0.000000
2:@0.406890:0.779574:0.420829:0.779574:0.420829:0.767105:0.406890:0.767105:0.000000
50:@0.420829:0.780078:0.437161:0.780078:0.437161:0.765794:0.420829:0.765794:0.000000:0.000000
5:@0.535473:0.718504:0.543639:0.718504:0.543639:0.704219:0.535473:0.704219:0.000000
10:@0.625434:0.718504:0.641766:0.718504:0.641766:0.704219:0.625434:0.704219:0.000000:0.000000
15:@0.719110:0.718504:0.735443:0.718504:0.735443:0.704219:0.719110:0.704219:0.000000:0.000000
50:@0.420913:0.639051:0.437245:0.639051:0.437245:0.624767:0.420913:0.624767:0.000000:0.000000
100:@0.412747:0.567302:0.437245:0.567302:0.437245:0.553018:0.412747:0.553018:0.000000:0.000000:0.000000
150:@0.412747:0.495680:0.437245:0.495680:0.437245:0.481395:0.412747:0.481395:0.000000:0.000000:0.000000
y:@0.432593:0.465207:0.439956:0.465207:0.439956:0.450923:0.432593:0.450923:0.000000
x:@0.806260:0.715957:0.813439:0.715957:0.813439:0.701673:0.806260:0.701673:0.000000
Máximo local:@0.301749:0.477863:0.390506:0.477863:0.390506:0.463578:0.301749:0.463578:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Mínimo relativo:@0.496816:0.775146:0.601367:0.775146:0.601367:0.760862:0.496816:0.760862:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Punto de corte eje :@0.454546:0.544544:0.581088:0.544544:0.581088:0.530259:0.454546:0.530259:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.581088:0.544544:0.587882:0.544544:0.587882:0.530511:0.581088:0.530511:0.000000
Puntos de corte eje :@0.369940:0.745456:0.502723:0.745456:0.502723:0.731172:0.369940:0.731172:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.502723:0.745456:0.509500:0.745456:0.509500:0.731424:0.502723:0.731424:0.000000
2:@0.233157:0.717316:0.247096:0.717316:0.247096:0.704847:0.233157:0.704847:0.000000
10:@0.247096:0.717820:0.263429:0.717820:0.263429:0.703536:0.247096:0.703536:0.000000:0.000000
(0, 105):@0.454464:0.558979:0.502574:0.558979:0.502574:0.544695:0.454464:0.544695:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( 5, 0):@0.296430:0.697737:0.342147:0.697737:0.342147:0.683452:0.296430:0.683452:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.300864:0.697232:0.314803:0.697232:0.314803:0.684764:0.300864:0.684764:0.000000
(3, 0):@0.511677:0.700334:0.543455:0.700334:0.543455:0.686050:0.511677:0.686050:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(7, 0):@0.582746:0.700334:0.614524:0.700334:0.614524:0.686050:0.582746:0.686050:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( 1,861, 135,20715):@0.268099:0.495828:0.401301:0.495828:0.401301:0.481544:0.268099:0.481544:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.272534:0.495324:0.286473:0.495324:0.286473:0.482855:0.272534:0.482855:0.000000
(5,19434,  40,39234):@0.559369:0.758870:0.700737:0.758870:0.700737:0.744586:0.559369:0.744586:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.622288:0.758366:0.636227:0.758366:0.636227:0.745897:0.622288:0.745897:0.000000
Figura 4.6- .:@0.866337:0.821554:0.926913:0.821554:0.926913:0.810127:0.866337:0.810127:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
4.3 Teorema de los ceros racionales de una función polinómica:@0.073089:0.854152:0.561910:0.854152:0.561910:0.837205:0.073089:0.837205:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sea  ( ) :@0.073089:0.891860:0.131624:0.891860:0.131624:0.876147:0.073089:0.876147:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.105025:0.891860:0.122383:0.891860:0.122383:0.876425:0.105025:0.876425:0.000000:0.000000:0.000000
5:@0.133078:0.891305:0.148411:0.891305:0.148411:0.877589:0.133078:0.877589:0.000000
 a x:@0.148614:0.891860:0.175596:0.891855:0.175596:0.876420:0.148614:0.876425:0.000000:0.000000:0.000000:0.000000
n:@0.162518:0.895028:0.168056:0.895028:0.168056:0.886029:0.162518:0.886029:0.000000
n:@0.175742:0.885791:0.181279:0.885791:0.181279:0.876792:0.175742:0.876792:0.000000
   :@0.181362:0.891855:0.206415:0.891855:0.206415:0.876142:0.181362:0.876142:0.000000:0.000000:0.000000
1:@0.186848:0.891300:0.202181:0.891300:0.202181:0.877584:0.186848:0.877584:0.000000
a:@0.207869:0.891855:0.217128:0.891855:0.217128:0.876420:0.207869:0.876420:0.000000
n:@0.217285:0.895028:0.222822:0.895028:0.222822:0.886029:0.217285:0.886029:0.000000
2:@0.222908:0.894704:0.231848:0.894704:0.231848:0.886708:0.222908:0.886708:0.000000
1:@0.231966:0.895028:0.237203:0.895028:0.237203:0.885867:0.231966:0.885867:0.000000
x:@0.237304:0.891855:0.244759:0.891855:0.244759:0.876420:0.237304:0.876420:0.000000
n:@0.244904:0.885791:0.250442:0.885791:0.250442:0.876792:0.244904:0.876792:0.000000
2:@0.250528:0.885467:0.259467:0.885467:0.259467:0.877471:0.250528:0.877471:0.000000
1 :@0.259585:0.885791:0.267279:0.885791:0.267279:0.876630:0.259585:0.876630:0.000000:0.000000
1:@0.268124:0.891300:0.283457:0.891300:0.283457:0.877584:0.268124:0.877584:0.000000
 :@0.283660:0.891855:0.287691:0.891855:0.287691:0.876142:0.283660:0.876142:0.000000
a:@0.289145:0.891855:0.298404:0.891855:0.298404:0.876420:0.289145:0.876420:0.000000
n:@0.298555:0.895028:0.304092:0.895028:0.304092:0.886029:0.298555:0.886029:0.000000
2:@0.304178:0.894704:0.313117:0.894704:0.313117:0.886708:0.304178:0.886708:0.000000
2:@0.313235:0.895028:0.318472:0.895028:0.318472:0.885867:0.313235:0.885867:0.000000
x:@0.318572:0.891855:0.326027:0.891855:0.326027:0.876420:0.318572:0.876420:0.000000
n:@0.326172:0.885791:0.331710:0.885791:0.331710:0.876792:0.326172:0.876792:0.000000
2:@0.331796:0.885467:0.340735:0.885467:0.340735:0.877471:0.331796:0.877471:0.000000
2 :@0.340853:0.885791:0.348547:0.885791:0.348547:0.876630:0.340853:0.876630:0.000000:0.000000
1:@0.349392:0.891300:0.364726:0.891300:0.364726:0.877584:0.349392:0.877584:0.000000
 … :@0.364928:0.891855:0.393036:0.891855:0.393036:0.876142:0.364928:0.876142:0.000000:0.000000:0.000000
1 :@0.394490:0.891300:0.414628:0.891300:0.414628:0.877584:0.394490:0.877584:0.000000:0.000000
a x:@0.416303:0.891855:0.438498:0.891855:0.438498:0.876420:0.416303:0.876420:0.000000:0.000000:0.000000
2:@0.425704:0.895028:0.430941:0.895028:0.430941:0.885867:0.425704:0.885867:0.000000
2  :@0.438644:0.885791:0.449536:0.885791:0.449536:0.876630:0.438644:0.876630:0.000000:0.000000:0.000000
1:@0.450388:0.891300:0.465721:0.891300:0.465721:0.877584:0.450388:0.877584:0.000000
 :@0.465924:0.891855:0.469955:0.891855:0.469955:0.876142:0.465924:0.876142:0.000000
a x:@0.471409:0.891855:0.493613:0.891855:0.493613:0.876420:0.471409:0.876420:0.000000:0.000000:0.000000
1:@0.480818:0.895028:0.486055:0.895028:0.486055:0.885867:0.480818:0.885867:0.000000
1 :@0.493757:0.885791:0.501451:0.885791:0.501451:0.876630:0.493757:0.876630:0.000000:0.000000
1:@0.502300:0.891300:0.517633:0.891300:0.517633:0.877584:0.502300:0.877584:0.000000
   una función polinómica de grado n con todos sus :@0.517835:0.891855:0.931096:0.891855:0.931096:0.876142:0.517835:0.876142:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.523321:0.891855:0.532580:0.891855:0.532580:0.876420:0.523321:0.876420:0.000000
0:@0.532730:0.895028:0.537967:0.895028:0.537967:0.885867:0.532730:0.885867:0.000000
coeficientes enteros. Si :@0.073084:0.914543:0.243924:0.914543:0.243924:0.898831:0.073084:0.898831:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.250530:0.905779:0.260210:0.905779:0.260210:0.889642:0.250530:0.889642:0.000000
q:@0.250530:0.922162:0.260210:0.922162:0.260210:0.906025:0.250530:0.906025:0.000000
 :@0.260210:0.922162:0.264424:0.922162:0.264424:0.905735:0.260210:0.905735:0.000000
 donde  ,      es un cero de la función, entonces   es un factor o divisor de   y   es un :@0.266494:0.914549:0.930964:0.914549:0.930964:0.898836:0.266494:0.898836:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p q:@0.323815:0.914549:0.349898:0.914549:0.349898:0.899114:0.323815:0.899114:0.000000:0.000000:0.000000
[:@0.354297:0.914410:0.369630:0.914410:0.369630:0.900362:0.354297:0.900362:0.000000
Z :@0.374030:0.913689:0.390891:0.913689:0.390891:0.900792:0.374030:0.900792:0.000000:0.000000
p:@0.647764:0.914549:0.657023:0.914549:0.657023:0.899114:0.647764:0.899114:0.000000
a:@0.842108:0.914549:0.851366:0.914549:0.851366:0.899114:0.842108:0.899114:0.000000
0:@0.851358:0.917721:0.856595:0.917721:0.856595:0.908561:0.851358:0.908561:0.000000
q:@0.873479:0.914549:0.882737:0.914549:0.882737:0.899114:0.873479:0.899114:0.000000
factor o divisor de  . :@0.073094:0.937237:0.228766:0.937242:0.228766:0.921530:0.073094:0.921525:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.206841:0.937237:0.216100:0.937237:0.216100:0.921802:0.206841:0.921802:0.000000
n:@0.216033:0.940415:0.221571:0.940415:0.221571:0.931416:0.216033:0.931416:0.000000
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