If and , and for , then the interval in which is decreasing…

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

Problem

f''(x)>0

and

f'(1)=0

, and

g(x)=f(\cot^2x+2\cot x+2)

for

0<x<\pi

, then the interval in which

g(x)

is decreasing is: (1)

(0,\pi)

(2)

\left(\dfrac{\pi}{2},\pi\right)

(3)

\left(\dfrac{3\pi}{4},\pi\right)

(4)

\left(0,\dfrac{3\pi}{4}\right)