The derivative of a differentiable function satisfies the following conditions: •…

MATHEMATICS · Single correct · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives

Problem

The derivative of a differentiable function

f

satisfies the following conditions: •

f'(x)=0

only at

x=-3

and

x=5

. •

f'(x)>0

for

-3<x<5

. •

f'(x)<0

for

x<-3

and for

x>5

. Which of the following accurately describes the behavior of

f

? (a)

f

is increasing on

(-\infty,-3)

and

(5,\infty)

and decreasing on

(-3,5)

. (b)

f

is decreasing on

(-\infty,-3)

and increasing on

(-3,5)

and

(5,\infty)

. (c)

f

is increasing on

(-3,5)

and decreasing on

(-\infty,-3)

and

(5,\infty)

. (d)

f

is decreasing on

(-\infty,-3)

, constant on

(-3,5)

, and increasing on

(5,\infty)