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Let g:R rarr R be a non constant twice d...

Let `g:R rarr R` be a non constant twice differentiable function such that `g'((1)/(2))=g'((3)/(2))` .If a real valued function `f` is defined as `f(x)=(1)/(2)[g(x)+g(2-x)]` ,then

A

`f'(x)=0` for atleast two `x in (0,2)`

B

`f'((3)/(2))+f'((1)/(2))=1`

C

`f''(x)=0` for no "x" in "(0,1)"

D

`f''(x)=0` for exactly one "x" in "(0,1)"

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