Let and for all

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

Problem

Let

g(x)=f(x)+f(1-x)

and

f''(x)>0

for all

x\in(0,1)

. Then

g(x)

is (1) increasing on

\left(0,\frac{1}{2}\right)

and decreasing on

\left(\frac{1}{2},1\right)

(2) increasing on

\left(\frac{1}{2},1\right)

and decreasing on

\left(0,\frac{1}{2}\right)

(3) increasing on

(0,1)

(4) decreasing on

(0,1)