180:@0.031627:0.974518:0.062330:0.974518:0.062330:0.956333:0.031627:0.956333:0.000000:0.000000:0.000000
Aplicaciones de la derivada:@0.073089:0.043661:0.316384:0.043661:0.316384:0.024916:0.073089:0.024916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ejemplo 4. :@0.293660:0.136836:0.381187:0.136836:0.381187:0.120167:0.293660:0.120167:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Realicemos un análisis de la curva  ( ) =  + 4 + 10 con respecto a la :@0.382806:0.136836:0.930876:0.136836:0.930876:0.120402:0.382806:0.120402:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.649785:0.136836:0.667180:0.136836:0.667180:0.120430:0.649785:0.120430:0.000000:0.000000:0.000000
x:@0.695012:0.136836:0.702467:0.136836:0.702467:0.120430:0.695012:0.120430:0.000000
4 :@0.702671:0.130772:0.710381:0.130772:0.710381:0.121191:0.702671:0.121191:0.000000:0.000000
x:@0.737417:0.136836:0.744872:0.136836:0.744872:0.120430:0.737417:0.120430:0.000000
3 :@0.745055:0.130772:0.752765:0.130772:0.752765:0.121191:0.745055:0.121191:0.000000:0.000000
concavidad, puntos de inflexión y máximos y mínimos relativos.:@0.293665:0.153478:0.754274:0.153478:0.754274:0.137044:0.293665:0.137044:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Paso 1. :@0.293665:0.189411:0.349785:0.189411:0.349785:0.172741:0.293665:0.172741:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Hallamos  ´( ) y  \( ) :@0.349678:0.189411:0.501465:0.189411:0.501465:0.172977:0.349678:0.172977:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f  x:@0.420841:0.189411:0.446409:0.189411:0.446409:0.173004:0.420841:0.173004:0.000000:0.000000:0.000000:0.000000
f  x:@0.467043:0.189411:0.492629:0.189411:0.492629:0.173004:0.467043:0.173004:0.000000:0.000000:0.000000:0.000000
f  x:@0.293647:0.216772:0.319214:0.216772:0.319214:0.200366:0.293647:0.200366:0.000000:0.000000:0.000000:0.000000
´( ) =  4 + 12      \( ) = 12 + 24 .:@0.301525:0.216772:0.556522:0.216778:0.556522:0.200344:0.301525:0.200339:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.355587:0.216772:0.363042:0.216772:0.363042:0.200366:0.355587:0.200366:0.000000
3 :@0.362990:0.210714:0.370534:0.210714:0.370534:0.201133:0.362990:0.201133:0.000000:0.000000
x:@0.403120:0.216778:0.410575:0.216778:0.410575:0.200371:0.403120:0.200371:0.000000
2:@0.410516:0.210714:0.415753:0.210714:0.415753:0.201133:0.410516:0.201133:0.000000
f  x:@0.431500:0.216778:0.457086:0.216778:0.457086:0.200371:0.431500:0.200371:0.000000:0.000000:0.000000:0.000000
x:@0.498411:0.216778:0.505866:0.216778:0.505866:0.200371:0.498411:0.200371:0.000000
2 :@0.505809:0.210714:0.513353:0.210714:0.513353:0.201133:0.505809:0.201133:0.000000:0.000000
x:@0.545938:0.216778:0.553393:0.216778:0.553393:0.200371:0.545938:0.200371:0.000000
Paso 2.:@0.293648:0.249146:0.345885:0.249146:0.345885:0.232476:0.293648:0.232476:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 Determinamos los puntos críticos haciendo  ´( ) = 0 y aplicamos el criterio de la :@0.345778:0.249146:0.931070:0.249146:0.931070:0.232712:0.345778:0.232712:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f  x:@0.669543:0.249146:0.695055:0.249146:0.695055:0.232740:0.669543:0.232740:0.000000:0.000000:0.000000:0.000000
segunda derivada 4 + 12 = 4  ( + 3) = 0, de donde se obtiene  = 0 y  =  3. :@0.293630:0.265788:0.874001:0.265781:0.874001:0.249348:0.293630:0.249354:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.436433:0.265788:0.443888:0.265788:0.443888:0.249382:0.436433:0.249382:0.000000
3 :@0.443855:0.259718:0.451399:0.259718:0.451399:0.250137:0.443855:0.250137:0.000000:0.000000
x:@0.483984:0.265781:0.491439:0.265781:0.491439:0.249375:0.483984:0.249375:0.000000
2 :@0.491381:0.259718:0.498925:0.259718:0.498925:0.250137:0.491381:0.250137:0.000000:0.000000
x x :@0.522620:0.265781:0.554635:0.265781:0.554635:0.249375:0.522620:0.249375:0.000000:0.000000:0.000000:0.000000
2:@0.530006:0.259718:0.535243:0.259718:0.535243:0.250137:0.530006:0.250137:0.000000
x :@0.772963:0.265781:0.783658:0.265781:0.783658:0.249375:0.772963:0.249375:0.000000:0.000000
x :@0.823270:0.265781:0.833965:0.265781:0.833965:0.249375:0.823270:0.249375:0.000000:0.000000
–:@0.848746:0.266364:0.857950:0.266364:0.857950:0.248710:0.848746:0.248710:0.000000
Para aplicar el criterio de la segunda derivada, evaluamos  \( ) en esos puntos críticos::@0.293675:0.296721:0.912680:0.296721:0.912680:0.280288:0.293675:0.280288:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f  x:@0.709513:0.296721:0.735100:0.296721:0.735100:0.280315:0.709513:0.280315:0.000000:0.000000:0.000000:0.000000
f :@0.293675:0.320505:0.301609:0.320505:0.301609:0.304099:0.293675:0.304099:0.000000:0.000000
\(0) = 0 y  \( 3) = 36.  :@0.301553:0.320505:0.457978:0.320505:0.457978:0.304072:0.301553:0.304072:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f :@0.369127:0.320505:0.377060:0.320505:0.377060:0.304099:0.369127:0.304099:0.000000:0.000000
–:@0.387258:0.321088:0.396461:0.321088:0.396461:0.303434:0.387258:0.303434:0.000000
Como  ´( 3) = 0 y  \( 3) > 0:@0.293675:0.355009:0.870039:0.355009:0.870039:0.338576:0.293675:0.338576:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f :@0.342344:0.355009:0.350277:0.355009:0.350277:0.338603:0.342344:0.338603:0.000000:0.000000
–:@0.360457:0.355592:0.369660:0.355592:0.369660:0.337938:0.360457:0.337938:0.000000
f :@0.426888:0.355009:0.434822:0.355009:0.434822:0.338603:0.426888:0.338603:0.000000:0.000000
–:@0.445020:0.355592:0.454223:0.355592:0.454223:0.337938:0.445020:0.337938:0.000000
f :@0.624527:0.355009:0.632461:0.355009:0.632461:0.338603:0.624527:0.338603:0.000000:0.000000
–:@0.637210:0.355592:0.646413:0.355592:0.646413:0.337938:0.637210:0.337938:0.000000
–:@0.674853:0.355592:0.684056:0.355592:0.684056:0.337938:0.674853:0.337938:0.000000
Nota.:@0.293675:0.385949:0.332165:0.385949:0.332165:0.369516:0.293675:0.369516:0.000000:0.000000:0.000000:0.000000:0.000000
 El criterio de la segunda derivada no aplica en  \(0) = 0. :@0.332054:0.385949:0.738671:0.385949:0.738671:0.369516:0.332054:0.369516:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f :@0.671852:0.385949:0.679786:0.385949:0.679786:0.369543:0.671852:0.369543:0.000000:0.000000
Paso 3. :@0.293675:0.421882:0.349795:0.421882:0.349795:0.405212:0.293675:0.405212:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Analizamos la concavidad. Para ello, nos apoyaremos en la siguiente tabla: :@0.349688:0.421882:0.888677:0.421882:0.888677:0.405448:0.349688:0.405448:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Intervalo:@0.330553:0.463113:0.401869:0.463113:0.401869:0.446166:0.330553:0.446166:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Valor de prueba:@0.441181:0.463113:0.566753:0.463113:0.566753:0.446166:0.441181:0.446166:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Signo de f\(x):@0.608558:0.463113:0.714799:0.463113:0.714799:0.446166:0.608558:0.446166:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Conclusión:@0.783721:0.463113:0.871265:0.463113:0.871265:0.446166:0.783721:0.446166:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( ∞, 2):@0.339720:0.500585:0.392696:0.500585:0.392696:0.484151:0.339720:0.484151:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
– –:@0.344524:0.501168:0.379001:0.501168:0.379001:0.483513:0.344524:0.483513:0.000000:0.000000:0.000000
x =  4:@0.481603:0.500585:0.526296:0.500585:0.526296:0.484151:0.481603:0.484151:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
–:@0.508202:0.501168:0.517405:0.501168:0.517405:0.483513:0.508202:0.483513:0.000000
f :@0.588899:0.500585:0.596833:0.500585:0.596833:0.484179:0.588899:0.484179:0.000000:0.000000
\( 4) = 96 > 0:@0.596777:0.500585:0.694281:0.500585:0.694281:0.484151:0.596777:0.484151:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
–:@0.607030:0.501168:0.616234:0.501168:0.616234:0.483513:0.607030:0.483513:0.000000
Cóncava hacia arriba:@0.747809:0.498976:0.898093:0.498976:0.898093:0.482543:0.747809:0.482543:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( 2,0):@0.346347:0.532440:0.386088:0.532440:0.386088:0.516007:0.346347:0.516007:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
–:@0.351151:0.533023:0.360355:0.533023:0.360355:0.515369:0.351151:0.515369:0.000000
x =  1:@0.481603:0.532440:0.526296:0.532440:0.526296:0.516007:0.481603:0.516007:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
–:@0.508202:0.533023:0.517405:0.533023:0.517405:0.515369:0.508202:0.515369:0.000000
f :@0.588899:0.532440:0.596833:0.532440:0.596833:0.516034:0.588899:0.516034:0.000000:0.000000
\( 1) =  12 < 0:@0.596777:0.532440:0.703355:0.532440:0.703355:0.516007:0.596777:0.516007:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
–:@0.607030:0.533023:0.616234:0.533023:0.616234:0.515369:0.607030:0.515369:0.000000
–:@0.648631:0.533023:0.657834:0.533023:0.657834:0.515369:0.648631:0.515369:0.000000
Cóncava hacia abajo:@0.747809:0.530846:0.896948:0.530846:0.896948:0.514412:0.747809:0.514412:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(0,∞):@0.348832:0.562715:0.383603:0.562715:0.383603:0.546281:0.348832:0.546281:0.000000:0.000000:0.000000:0.000000:0.000000
 x= 1:@0.486150:0.562715:0.521768:0.562715:0.521768:0.546281:0.486150:0.546281:0.000000:0.000000:0.000000:0.000000:0.000000
f :@0.588899:0.562715:0.596833:0.562715:0.596833:0.546309:0.588899:0.546309:0.000000:0.000000
\(1) = 36 > 0:@0.596777:0.562715:0.685187:0.562715:0.685187:0.546281:0.596777:0.546281:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Cóncava hacia arriba:@0.747809:0.562715:0.898093:0.562715:0.898093:0.546281:0.747809:0.546281:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Paso 4. :@0.293647:0.604652:0.349767:0.604652:0.349767:0.587982:0.293647:0.587982:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Determinamos los puntos de inflexión.:@0.349660:0.604652:0.630507:0.604652:0.630507:0.588218:0.349660:0.588218:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Hacemos  \( ) = 0 para encontrar los posibles puntos de inflexión.:@0.293647:0.632014:0.770479:0.632014:0.770479:0.615580:0.293647:0.615580:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f  x:@0.365858:0.632014:0.391444:0.632014:0.391444:0.615608:0.365858:0.615608:0.000000:0.000000:0.000000:0.000000
f  x:@0.293647:0.659376:0.318497:0.659376:0.318497:0.642970:0.293647:0.642970:0.000000:0.000000:0.000000:0.000000
\( ) = 12 + 24 = (12 )( + 2) = 0 de donde se concluye para  = 0 y para  =  2  ”( ) = 0. :@0.301157:0.659376:0.925782:0.659387:0.925782:0.642953:0.301157:0.642942:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.358532:0.659376:0.365987:0.659376:0.365987:0.642970:0.358532:0.642970:0.000000
2 :@0.365751:0.653323:0.373188:0.653323:0.373188:0.643742:0.365751:0.643742:0.000000:0.000000
x :@0.404930:0.659387:0.415441:0.659387:0.415441:0.642981:0.404930:0.642981:0.000000:0.000000
x x :@0.451722:0.659387:0.478651:0.659387:0.478651:0.642981:0.451722:0.642981:0.000000:0.000000:0.000000:0.000000
x :@0.732506:0.659387:0.743016:0.659387:0.743016:0.642981:0.732506:0.642981:0.000000:0.000000
x :@0.816351:0.659387:0.826861:0.659387:0.826861:0.642981:0.816351:0.642981:0.000000:0.000000
–:@0.841090:0.659970:0.850294:0.659970:0.850294:0.642316:0.841090:0.642316:0.000000
f  x:@0.862498:0.659387:0.887200:0.659387:0.887200:0.642981:0.862498:0.642981:0.000000:0.000000:0.000000:0.000000
En este caso, ambos son puntos de inflexión, como lo podemos :@0.459176:0.686749:0.930976:0.686749:0.930976:0.670315:0.459176:0.670315:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
analizar en la tabla del paso 3.:@0.459176:0.703391:0.668633:0.703391:0.668633:0.686957:0.459176:0.686957:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Paso 5.:@0.459176:0.739324:0.511468:0.739324:0.511468:0.722654:0.459176:0.722654:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.511361:0.739324:0.515392:0.739324:0.515392:0.722890:0.511361:0.722890:0.000000
Elaboramos la gráfica.:@0.515319:0.739324:0.672430:0.739324:0.672430:0.722890:0.515319:0.722890:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Aquí presentamos la gráfica de la función hecha con la calculado-:@0.459176:0.766686:0.926886:0.766686:0.926886:0.750252:0.459176:0.750252:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ra gráfica Desmos (Figura 3.4). :@0.459176:0.783327:0.678799:0.783327:0.678799:0.766894:0.459176:0.766894:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
      Figura 3.4:@0.061704:0.699864:0.138326:0.699864:0.138326:0.686418:0.061704:0.686418:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Mínimo relativo:@0.101470:0.927662:0.188225:0.927662:0.188225:0.915876:0.101470:0.915876:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Punto de inexión:@0.265751:0.800140:0.367279:0.800140:0.367279:0.788354:0.265751:0.788354:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Punto de inexión:@0.190369:0.856398:0.261210:0.856398:0.261210:0.847231:0.190369:0.847231:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Cóncava hacia arriba:@0.267891:0.825320:0.347773:0.825320:0.347773:0.816153:0.267891:0.816153:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.231372:0.737915:0.238272:0.737915:0.238272:0.723734:0.231372:0.723734:0.000000
x:@0.362518:0.851515:0.369418:0.851515:0.369418:0.837334:0.362518:0.837334:0.000000
2:@0.335272:0.841770:0.341839:0.841770:0.341839:0.830177:0.335272:0.830177:0.000000
-4:@0.099265:0.841770:0.109763:0.841770:0.109763:0.830177:0.099265:0.830177:0.000000:0.000000
-2:@0.177712:0.841770:0.188210:0.841770:0.188210:0.830177:0.177712:0.830177:0.000000:0.000000
0:@0.252217:0.841770:0.258784:0.841770:0.258784:0.830177:0.252217:0.830177:0.000000
-20:@0.241284:0.916786:0.258349:0.916786:0.258349:0.905193:0.241284:0.905193:0.000000:0.000000:0.000000
20:@0.244677:0.752286:0.257811:0.752286:0.257811:0.740693:0.244677:0.740693:0.000000:0.000000
y = x:@0.324154:0.740917:0.352974:0.740917:0.352974:0.726736:0.324154:0.726736:0.000000:0.000000:0.000000:0.000000:0.000000
4 :@0.352973:0.737166:0.362254:0.737166:0.362254:0.725573:0.352973:0.725573:0.000000:0.000000
+4  +10:@0.362254:0.740917:0.421768:0.740917:0.421768:0.726747:0.362254:0.726747:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.379605:0.740917:0.386505:0.740917:0.386505:0.726736:0.379605:0.726736:0.000000
3:@0.386505:0.737166:0.393072:0.737166:0.393072:0.725573:0.386505:0.725573:0.000000
(0,-10):@0.211388:0.783467:0.255817:0.783467:0.255817:0.768010:0.211388:0.768010:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(-2,-6):@0.198587:0.871337:0.239500:0.871337:0.239500:0.855880:0.198587:0.855880:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(-3,-17):@0.120362:0.916474:0.169980:0.916474:0.169980:0.901017:0.120362:0.901017:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Cóncava hacia abajo:@0.182546:0.825321:0.261592:0.825321:0.261592:0.816154:0.182546:0.816154:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Cóncava hacia arriba:@0.102892:0.825321:0.182775:0.825321:0.182775:0.816154:0.102892:0.816154:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Nota.:@0.488141:0.841064:0.528506:0.841064:0.528506:0.824395:0.488141:0.824395:0.000000:0.000000:0.000000:0.000000:0.000000
 Con toda la información obtenida en los cuatro :@0.528343:0.841064:0.871531:0.841064:0.871531:0.824631:0.528343:0.824631:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
primeros pasos se puede hacer un bosquejo de la :@0.488141:0.857706:0.871936:0.857706:0.871936:0.841272:0.488141:0.841272:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
gráfica sin necesidad de usar la calculadora gráfica.:@0.488141:0.874348:0.854722:0.874348:0.854722:0.857914:0.488141:0.857914:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Estabilidad estructural :@0.078581:0.238891:0.236021:0.238891:0.236021:0.223737:0.078581:0.223737:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
en ingeniería: :@0.078581:0.254020:0.175918:0.254020:0.175918:0.238866:0.078581:0.238866:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
en el :@0.175788:0.254020:0.211598:0.254020:0.211598:0.239080:0.175788:0.239080:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
diseño de puentes, arcos :@0.078581:0.269149:0.246050:0.269149:0.246050:0.254209:0.078581:0.254209:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
o edificios es importante :@0.078581:0.284278:0.245220:0.284278:0.245220:0.269338:0.078581:0.269338:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
saber si una estructura :@0.078581:0.299407:0.230668:0.299407:0.230668:0.284467:0.078581:0.284467:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tiene una curvatura :@0.078581:0.314536:0.211224:0.314536:0.211224:0.299596:0.078581:0.299596:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
que la haga estable. Las :@0.078581:0.329665:0.237948:0.329665:0.237948:0.314725:0.078581:0.314725:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
secciones cóncavas hacia :@0.078581:0.344794:0.249862:0.344794:0.249862:0.329854:0.078581:0.329854:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
arriba tienden a soportar :@0.078581:0.359923:0.245548:0.359923:0.245548:0.344983:0.078581:0.344983:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cargas de mejor manera, :@0.078581:0.375051:0.244844:0.375051:0.244844:0.360112:0.078581:0.360112:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
mientras que las cóncavas :@0.078581:0.390180:0.255014:0.390180:0.255014:0.375241:0.078581:0.375241:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
hacia abajo pueden :@0.078581:0.405309:0.212904:0.405309:0.212904:0.390370:0.078581:0.390370:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ser más vulnerables a :@0.078581:0.420438:0.223086:0.420438:0.223086:0.405498:0.078581:0.405498:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
deformaciones o colapsos.:@0.078581:0.435567:0.253850:0.435567:0.253850:0.420627:0.078581:0.420627:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Interdisciplinariedad :@0.078581:0.174280:0.244955:0.174280:0.244955:0.157333:0.078581:0.157333:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Matemática e :@0.078581:0.190922:0.181610:0.190922:0.181610:0.174488:0.078581:0.174488:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ingeniería:@0.078581:0.207564:0.150969:0.207564:0.150969:0.191130:0.078581:0.191130:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Un punto ( ,   ( )) de la :@0.082576:0.600463:0.234236:0.600463:0.234236:0.585523:0.082576:0.585523:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
c f c:@0.154115:0.600463:0.186545:0.600463:0.186545:0.585548:0.154115:0.585548:0.000000:0.000000:0.000000:0.000000:0.000000
curva   =  ( ) es un punto :@0.082544:0.615592:0.253373:0.615592:0.253373:0.600652:0.082544:0.600652:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.122722:0.615592:0.129516:0.615592:0.129516:0.600677:0.122722:0.600677:0.000000
f x:@0.146534:0.615592:0.161879:0.615592:0.161879:0.600677:0.146534:0.600677:0.000000:0.000000:0.000000
de inflexión si se cumple :@0.082544:0.630720:0.248594:0.630720:0.248594:0.615781:0.082544:0.615781:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
que  '' ( ) = 0 o   ''( ) no :@0.082544:0.645849:0.236663:0.645849:0.236663:0.630910:0.082544:0.630910:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f c:@0.111979:0.645849:0.136896:0.645849:0.136896:0.630935:0.111979:0.630935:0.000000:0.000000:0.000000
f c:@0.182378:0.645849:0.207295:0.645849:0.207295:0.630935:0.182378:0.630935:0.000000:0.000000:0.000000
existe.:@0.082494:0.660978:0.123045:0.660978:0.123045:0.646039:0.082494:0.646039:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
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