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Let f be a twice differentiable function...

Let f be a twice differentiable function such that `f''(x)gt 0 AA x in R`. Let h(x) is defined by `h(x)=f(sin^(2)x)+f(cos^(2)x)` where `|x|lt (pi)/(2)`.
The number of critical points of h(x) are

A

1

B

2

C

3

D

more than 3

Text Solution

Verified by Experts

The correct Answer is:
C
`f''(x)gt0 rArr f'(x)` is an increasing function
`h'(x)=sin2x(f'(sin^(2)x)-f'(cos^(2)x))`
`f'(x)=0 rArr sin^(2)x=0 rArr x=0`
or `f'(sin^(2)x)=f'(cos^(2)x) rArr sin^(2)x=cos^(2)x rArr tan^(2)x=1 rArr x = pm(pi)/(4)`
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