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Max y Mín de Integrales

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Max y Mín de Integrales

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Extremos de funciones con integrales

Created by

Mar
Mar
Mexico

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Max y Mín de Integrales
 

Max y Mín de IntegralesOnline version

Extremos de funciones con integrales

by Mar
1

Sea F(x)=∫_0^x (t^2-4) dt. ¿En qué x tiene F su máximo local?

2

Sea F(x)=∫_0^x (t^3-6t) dt. ¿Dónde se produce un máximo local de F?

3

Para F(x)=∫_a^x f(t) dt, ¿qué condición da un extremo de F?

4

Sea F(x)=∫_0^x sin t dt. ¿En qué x tiene F su máximo en [0, 2π]?

5

Si F(x)=∫_0^x cos t dt, ¿dónde F tiene un extremo y cuál es?

6

Para H(x)=∫_0^x e^{-t^2} dt, ¿hay puntos críticos?

7

Si F'(x)=f(x) y f(x)≥0 para todo x, ¿cómo es F?

8

Sea G(a)=∫_0^1 (a t^2 - t) dt. ¿Cómo varía G respecto a a?

9

Aplicando el Teorema del Valor Medio para integrales, existe c en [a,b] tal que:

10

Si F'(x0)=0 y F''(x0)>0, ¿qué tipo de extremo es F en x0?

 
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