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Let f (x) be a twice differentiable func...

Let f (x) be a twice differentiable function defined on `(-oo,oo)` such that `f (x) =f (2-x)and f '((1)/(2 )) =f' ((1)/(4))=0.` Then
`int _(-1) ^(1) f'(1+ x ) x ^(2) e ^(x ^(2))dx` is equal to :

A

g(x) is increasing in `(-oo, (1)/(4))`

B

g(x) attains local minima at `x=(1)/(2)`

C

minimum number of zeroes f `g''(x)` is 2 in [0, 1]

D

`g'(x) lt 0 " in "((1)/(2), oo)`

Text Solution

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The correct Answer is:
A,C,D
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