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Let g(x)=log(f(x)), where f(x) is a twic...

Let `g(x)=log(f(x))`, where `f(x)` is a twice differentiable positive function on `(0,oo)`, such that `f(x+1)=xf(x)`.
Then for `N=1,2,3, . . .. . . .. . . g'(N+1/2)-g''((1)/(2))=`

A

`-4{1+(1)/(9)+(1)/(25)+ . . . +(1)/((2N-1)^(2))}`

B

`4{1+(1)/(9)+(1)/(25)+ . . . .. +(1)/((2N-1)^(2))}`

C

`-4{1+1/9+1/(25)+ . . . .. +(1)/((2N+1)^(2))}`

D

`4{1+(1)/(9)+(1)/(25)+ . . . . . +(1)/((2N+1)^(2))}`.

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The correct Answer is:
A
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