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h(x)=3f((x^2)/3)+f(3-x^2)AAx in (-3, 4) ...

`h(x)=3f((x^2)/3)+f(3-x^2)AAx in (-3, 4)` where `f''(x)> 0 AA x in (-3,4),` then h(x ) is

A

increasing in`((3)/(4),4)`

B

decreasing in `(-3,-(3)/(2))`

C

increasing in `(-3)/(2),0))`

D

decreasing in `(0, (3)/(2))`

Text Solution

Verified by Experts

The correct Answer is:
1
`phi(x) 3f((x^(2))/(3)) (2x)/(3) - 2x f(3-x^(2))`
`2x[f((x^(2))/(3)) -f(3 - x^(2))]`
`phi(x) = 0 rArr (x^(2))/(3) = 3 - x^(2)`
or `x =pm 3//2`
`f(x) gt 0`,
`rArrf(x)` is increasing
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