208:@0.054582:0.966558:0.078778:0.966558:0.078778:0.950778:0.054582:0.950778:0.000000:0.000000:0.000000
Proyecto interdisciplinario:@0.321675:0.079753:0.815528:0.079753:0.815528:0.012764:0.321675:0.012764:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Áreas relacionadas: Matemática y Economía:@0.426319:0.092454:0.710906:0.092454:0.710906:0.077391:0.426319:0.077391:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Tema:Maximización :@0.143847:0.146660:0.363806:0.146660:0.363806:0.107956:0.143847:0.107956:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de costos y derivadas:@0.143847:0.179350:0.369512:0.179350:0.369512:0.140645:0.143847:0.140645:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Shutterstock, 83105218:@0.121958:0.899691:0.121958:0.834844:0.110490:0.834844:0.110490:0.899691:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Objetivos:@0.153344:0.216082:0.230599:0.216082:0.230599:0.198400:0.153344:0.198400:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
•:@0.153344:0.233498:0.161108:0.233498:0.161108:0.216307:0.153344:0.216307:0.000000
  Comprender los concep-:@0.161108:0.232790:0.349850:0.232790:0.349850:0.216292:0.161108:0.216292:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tos básicos del cálculo :@0.172339:0.250141:0.333973:0.250141:0.333973:0.233643:0.172339:0.233643:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
diferencial.:@0.172339:0.267491:0.247320:0.267491:0.247320:0.250994:0.172339:0.250994:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
•:@0.153344:0.285551:0.161108:0.285551:0.161108:0.268359:0.153344:0.268359:0.000000
  Iniciarse de manera natu-:@0.161108:0.284842:0.361486:0.284842:0.361486:0.268344:0.161108:0.268344:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ral en el manejo de deri-:@0.177079:0.302193:0.361524:0.302193:0.361524:0.285695:0.177079:0.285695:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
vadas y darse cuenta de la :@0.177079:0.319544:0.365626:0.319544:0.365626:0.303046:0.177079:0.303046:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
necesidad de usarlas para :@0.177079:0.336894:0.365626:0.336894:0.365626:0.320397:0.177079:0.320397:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
encontrar la solución de :@0.177079:0.354245:0.365647:0.354245:0.365647:0.337748:0.177079:0.337748:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
problemas reales.:@0.177079:0.371596:0.298929:0.371596:0.298929:0.355098:0.177079:0.355098:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
•:@0.153344:0.389655:0.161108:0.389655:0.161108:0.372463:0.153344:0.372463:0.000000
  Valorar la utilidad de sus :@0.161108:0.388947:0.365653:0.388947:0.365653:0.372449:0.161108:0.372449:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
conocimientos sobre de-:@0.177079:0.406297:0.361486:0.406297:0.361486:0.389800:0.177079:0.389800:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
rivadas y encontrar usos :@0.177079:0.423648:0.365647:0.423648:0.365647:0.407151:0.177079:0.407151:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
adecuados en situaciones :@0.177079:0.440999:0.365626:0.440999:0.365626:0.424501:0.177079:0.424501:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de la vida real.:@0.177079:0.458350:0.276237:0.458350:0.276237:0.441852:0.177079:0.441852:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Justificación:@0.404235:0.124058:0.502696:0.124058:0.502696:0.106375:0.404235:0.106375:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
La importancia del estudio de las derivadas radica en la posibilidad de :@0.404235:0.140766:0.895894:0.140766:0.895894:0.124268:0.404235:0.124268:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
resolver situaciones en diversos ámbitos. Por ejemplo, en economía, en :@0.404235:0.158116:0.895934:0.158116:0.895934:0.141619:0.404235:0.141619:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
temas como costos, consumo, demanda, utilidad, ahorro o maximiza-:@0.404235:0.175467:0.891736:0.175467:0.891736:0.158969:0.404235:0.158969:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ción de la producción.:@0.404235:0.192818:0.558526:0.192818:0.558526:0.176320:0.404235:0.176320:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Actividades:@0.404235:0.211566:0.498575:0.211566:0.498575:0.193883:0.404235:0.193883:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
•:@0.404235:0.228982:0.411998:0.228982:0.411998:0.211790:0.404235:0.211790:0.000000
  Formar equipos de trabajo, con no más de tres estudiantes por grupo.:@0.411998:0.228274:0.891703:0.228274:0.891703:0.211776:0.411998:0.211776:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
•:@0.404235:0.246333:0.411998:0.246333:0.411998:0.229141:0.404235:0.229141:0.000000
  Analizar el problema planteado como modelo y proponer una  :@0.411998:0.245624:0.895903:0.245624:0.895903:0.229127:0.411998:0.229127:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
situación similar.:@0.427969:0.262975:0.543850:0.262975:0.543850:0.246478:0.427969:0.246478:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Recursos:@0.404235:0.281723:0.475640:0.281723:0.475640:0.264041:0.404235:0.264041:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Modelo de problema resuelto:@0.404235:0.298894:0.631561:0.298894:0.631561:0.281948:0.404235:0.281948:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
La gerente comercial de una empresa editorial estima que si el precio :@0.404235:0.315782:0.895957:0.315782:0.895957:0.299284:0.404235:0.299284:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de un libro es de $ 20, vende 10 000 ejemplares. Por cada dólar que se :@0.404235:0.333133:0.895843:0.333133:0.895843:0.316635:0.404235:0.316635:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
incremente el precio, las ventas disminuyen en 400 ejemplares. ¿Qué :@0.404235:0.350483:0.895901:0.350483:0.895901:0.333986:0.404235:0.333986:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
precio deberá fijar a cada libro, de manera que el ingreso para la em-:@0.404235:0.367834:0.891848:0.367834:0.891848:0.351336:0.404235:0.351336:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
presa por la venta de estos libros sea el máximo? ¿Cuál es el valor de :@0.404235:0.385185:0.895899:0.385185:0.895899:0.368687:0.404235:0.368687:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
dicho ingreso?:@0.404235:0.402536:0.505895:0.402536:0.505895:0.386038:0.404235:0.386038:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Solución :@0.404235:0.420349:0.477943:0.420349:0.477943:0.403403:0.404235:0.403403:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
: Los ingresos se calculan multiplicando el precio por el nú-:@0.471162:0.419886:0.891757:0.419886:0.891757:0.403389:0.471162:0.403389:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
mero de ejemplares vendidos.:@0.404254:0.437237:0.615937:0.437237:0.615937:0.420739:0.404254:0.420739:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
L :@0.404254:0.454704:0.416237:0.454704:0.416237:0.438235:0.404254:0.438235:0.000000:0.000000
= 20   10 000, donde   es el ingreso.:@0.416237:0.454588:0.670549:0.454588:0.670549:0.438090:0.416237:0.438090:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
×:@0.452300:0.452850:0.461699:0.452850:0.461699:0.438504:0.452300:0.438504:0.000000
L:@0.570391:0.454704:0.578232:0.454704:0.578232:0.438235:0.570391:0.438235:0.000000
Si x representa el número de dólares que se incrementa al precio :@0.404230:0.471939:0.895922:0.471939:0.895922:0.455441:0.404230:0.455441:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.891757:0.471939:0.895899:0.471939:0.895899:0.455441:0.891757:0.455441:0.000000
de cada ejemplar, entonces 20 +  es el nuevo precio del libro y :@0.404230:0.489289:0.895936:0.489289:0.895936:0.472792:0.404230:0.472792:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 x:@0.648339:0.489405:0.663173:0.489405:0.663173:0.472936:0.648339:0.472936:0.000000:0.000000
 :@0.891757:0.489289:0.895899:0.489289:0.895899:0.472792:0.891757:0.472792:0.000000
10 000 – 4 000x es el nuevo número de ejemplares vendidos.:@0.404230:0.506640:0.834321:0.506640:0.834321:0.490142:0.404230:0.490142:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
La función que representa el ingreso en términos del número de dó-:@0.404230:0.523991:0.891809:0.523991:0.891809:0.507493:0.404230:0.507493:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
lares en que se aumenta el precio del libro es::@0.404230:0.541342:0.723047:0.541342:0.723047:0.524844:0.404230:0.524844:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
L  x:@0.404230:0.558808:0.429641:0.558808:0.429641:0.542339:0.404230:0.542339:0.000000:0.000000:0.000000:0.000000
( ) = (20 +  )(10 000 – 400 ).:@0.416213:0.558692:0.623180:0.558692:0.623180:0.542195:0.416213:0.542195:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.496723:0.558808:0.504198:0.558808:0.504198:0.542339:0.496723:0.542339:0.000000
x:@0.606997:0.558808:0.614472:0.558808:0.614472:0.542339:0.606997:0.542339:0.000000
Esta función :@0.404230:0.576043:0.497551:0.576043:0.497551:0.559545:0.404230:0.559545:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
I(x), :@0.498611:0.576159:0.527952:0.576159:0.527952:0.559690:0.498611:0.559690:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
recibe el nombre de función objetivo porque es la :@0.529031:0.576043:0.895859:0.576043:0.895859:0.559545:0.529031:0.559545:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
función que se requiere :@0.404230:0.593394:0.575150:0.593394:0.575150:0.576896:0.404230:0.576896:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
optimizar:@0.575150:0.593611:0.647048:0.593611:0.647048:0.576896:0.575150:0.576896:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
. La derivada de la función :@0.647050:0.593394:0.836038:0.593394:0.836038:0.576896:0.647050:0.576896:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
I(x):@0.836038:0.593510:0.858386:0.593510:0.858386:0.577041:0.836038:0.577041:0.000000:0.000000:0.000000:0.000000
 es::@0.858386:0.593394:0.879942:0.593394:0.879942:0.576896:0.858386:0.576896:0.000000:0.000000:0.000000:0.000000
L´ x:@0.404230:0.610860:0.433205:0.610860:0.433205:0.594392:0.404230:0.594392:0.000000:0.000000:0.000000:0.000000
( ) = (1)(10 000 – 400 ) – 400(20 +  ),:@0.419777:0.610745:0.691417:0.610745:0.691417:0.594247:0.419777:0.594247:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.575498:0.610860:0.582973:0.610860:0.582973:0.594392:0.575498:0.594392:0.000000
x:@0.675235:0.610860:0.682710:0.610860:0.682710:0.594392:0.675235:0.594392:0.000000
L´ x:@0.404230:0.628211:0.433205:0.628211:0.433205:0.611742:0.404230:0.611742:0.000000:0.000000:0.000000:0.000000
( ) = 10 000 – 400  – 8 000 – 400 :@0.419777:0.628095:0.661942:0.628095:0.661942:0.611598:0.419777:0.611598:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.549144:0.628211:0.556618:0.628211:0.556618:0.611742:0.549144:0.611742:0.000000
x,:@0.661942:0.628211:0.672383:0.628211:0.672383:0.611742:0.661942:0.611742:0.000000:0.000000
L´ x:@0.404230:0.645562:0.433205:0.645562:0.433205:0.629093:0.404230:0.629093:0.000000:0.000000:0.000000:0.000000
( ) = –8 00  + 2 000,:@0.419777:0.645446:0.565827:0.645446:0.565827:0.628948:0.419777:0.628948:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.498380:0.645562:0.505855:0.645562:0.505855:0.629093:0.498380:0.629093:0.000000
L´ x:@0.404230:0.662913:0.433205:0.662913:0.433205:0.646444:0.404230:0.646444:0.000000:0.000000:0.000000:0.000000
( ) = 0   800   = 2 000,:@0.419777:0.662797:0.591123:0.662797:0.591123:0.646299:0.419777:0.646299:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
⇒:@0.470888:0.663346:0.489903:0.663346:0.489903:0.644506:0.470888:0.644506:0.000000
x:@0.523675:0.662913:0.531150:0.662913:0.531150:0.646444:0.523675:0.646444:0.000000
x:@0.408265:0.688436:0.415740:0.688436:0.415740:0.671967:0.408265:0.671967:0.000000
=:@0.419362:0.688956:0.429939:0.688956:0.429939:0.672676:0.419362:0.672676:0.000000
2000:@0.435044:0.679486:0.470608:0.679486:0.470608:0.662988:0.435044:0.662988:0.000000:0.000000:0.000000:0.000000
800:@0.440008:0.699680:0.465341:0.699680:0.465341:0.683182:0.440008:0.683182:0.000000:0.000000:0.000000
;:@0.473491:0.688320:0.476246:0.688320:0.476246:0.671822:0.473491:0.671822:0.000000
x:@0.478365:0.688436:0.485840:0.688436:0.485840:0.671967:0.478365:0.671967:0.000000
=:@0.489461:0.688956:0.500038:0.688956:0.500038:0.672676:0.489461:0.672676:0.000000
2,5 .:@0.502600:0.688320:0.530297:0.688320:0.530297:0.671822:0.502600:0.671822:0.000000:0.000000:0.000000:0.000000:0.000000
Recordemos que x representa el número de dólares en que se debe :@0.404225:0.718250:0.895869:0.718250:0.895869:0.701752:0.404225:0.701752:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
incrementar el precio del libro para obtener el ingreso máximo.:@0.404225:0.735601:0.850480:0.735601:0.850480:0.719103:0.404225:0.719103:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
De esta manera, al incrementar el precio de venta del libro en $ 2,5, se :@0.404225:0.752952:0.895794:0.752952:0.895794:0.736454:0.404225:0.736454:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
obtiene el ingreso máximo. Para calcular el ingreso máximo se susti-:@0.404225:0.770302:0.891712:0.770302:0.891712:0.753805:0.404225:0.753805:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tuye   en la función  (x).:@0.404225:0.787653:0.578171:0.787653:0.578171:0.771156:0.404225:0.771156:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.439442:0.787769:0.446917:0.787769:0.446917:0.771300:0.439442:0.771300:0.000000
L:@0.547674:0.787769:0.555515:0.787769:0.555515:0.771300:0.547674:0.771300:0.000000
L :@0.404225:0.805120:0.416208:0.805120:0.416208:0.788651:0.404225:0.788651:0.000000:0.000000
(2,5) = (20 + 2,5) [10 000 – 400(2,5)]:@0.416208:0.805004:0.673091:0.805004:0.673091:0.788506:0.416208:0.788506:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
L :@0.404225:0.822470:0.416208:0.822470:0.416208:0.806002:0.404225:0.806002:0.000000:0.000000
(2,5) = (22,5) [10 000 – (1 000):@0.416208:0.822355:0.632538:0.822355:0.632538:0.805857:0.416208:0.805857:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
L :@0.404225:0.839821:0.416208:0.839821:0.416208:0.823352:0.404225:0.823352:0.000000:0.000000
(2,5) = 202 500,00:@0.416208:0.839705:0.541818:0.839705:0.541818:0.823208:0.416208:0.823208:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Este valor representa el máximo ingreso.:@0.404225:0.857056:0.688172:0.857056:0.688172:0.840559:0.404225:0.840559:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Adaptado de http://www.mat.uson.mx/~jldiaz/contenido_Derivadas.html:@0.478466:0.874354:0.891769:0.874354:0.891769:0.861442:0.478466:0.861442:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Conclusiones:@0.404235:0.893903:0.510677:0.893903:0.510677:0.876221:0.404235:0.876221:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Es importante recuperar la importancia de realizar cálculos reales :@0.404235:0.910611:0.895953:0.910611:0.895953:0.894113:0.404235:0.894113:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cuando se trata de emprender una empresa.:@0.404235:0.927962:0.718813:0.927962:0.718813:0.911464:0.404235:0.911464:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Glosario:@0.199644:0.554176:0.267109:0.554176:0.267109:0.536493:0.199644:0.536493:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
optimizar:@0.199880:0.580989:0.264117:0.580989:0.264117:0.565728:0.199880:0.565728:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
. Buscar la :@0.263943:0.580791:0.329359:0.580791:0.329359:0.565728:0.263943:0.565728:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
mejor manera de realizar una :@0.153337:0.596633:0.341250:0.596633:0.341250:0.581570:0.153337:0.581570:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
actividad.:@0.153337:0.612475:0.213442:0.612475:0.213442:0.597412:0.153337:0.597412:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.146908:0.557907:0.158313:0.556398:0.153110:0.534253:0.141706:0.535762:0.000000
c:@0.150290:0.568877:0.160889:0.567474:0.155807:0.545839:0.145207:0.547242:0.000000
b:@0.160665:0.561659:0.173379:0.559976:0.168247:0.538134:0.155534:0.539816:0.000000