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Derivadas y límites: extremos y continuidad

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Derivadas y límites: extremos y continuidad

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Quiz sobre extremos por segunda derivada y límites

Created by

CARLOS REMIGIO SANCHEZ OCHOA
CARLOS REMIGIO SANCHEZ OCHOA
Ecuador

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Derivadas y límites: extremos y continuidad
 

Derivadas y límites: extremos y continuidadOnline version

Quiz sobre extremos por segunda derivada y límites

by CARLOS REMIGIO SANCHEZ OCHOA
1

Si f'(a)=0 y f''(a)>0, ¿qué extremo tiene f en a?

2

Si f'(a)=0 y f''(a)<0, ¿qué extremo hay en a?

3

¿Qué dice la prueba de la segunda derivada cuando f''(a)=0?

4

Para f(x)=x^3, ¿tiene extremo en x=0?

5

Si f es continua en c, ¿qué sabemos sobre lim_{x→c} f(x}?

6

¿Qué condición garantiza continuidad en c?

7

Si lim_{x→2} f(x)=3 y f es continua en 2, ¿qué es f(2)?

Explicación

f''(a)>0 indica curvatura hacia arriba, extremo mínimo local en a.

La segunda derivada negativa sugiere concavidad hacia abajo, extremo máximo local.

Con f''(a)=0 la prueba es inconclusa; se requieren otros métodos.

x^3 tiene pendiente 0 en 0 pero no extrema; es punto de inflexión.

Continuidad en c implica que el límite por x→c es f(c).

Continuidad requiere límites laterales existan y equal f(c).

Continua en 2 implica f(2)=lim_{x→2} f(x)=3.

 
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