The derivative of a function satisfies for for

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

Problem

The derivative of a function

g

satisfies

g'(x)>0

for

x<-1

g'(x)<0

for

-1<x<4

, and

g'(x)>0

for

x>4

. Which one of the following statements is correct? (a)

g

is decreasing on

(-\infty,-1)

\;and\;

(4,\infty)

(b)

g

is increasing on

(-\infty,-1)

\;and\;

(4,\infty)

(c)

g

is increasing on

(-1,4)

\;only (d)

g

is decreasing on

(-\infty,4)

\;and\;increasing on\;

(4,\infty)