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Let g(x)=f(x)+f(1-x) and f''(x) gt 0,x i...

Let `g(x)=f(x)+f(1-x)` and `f''(x) gt 0,x in (0,1)`. If `g` is decreasing in the interval `(0,alpha)` and increasing in the interval `(alpha,1)`, then `tan^(-1)(2alpha)+tan^(-1)(1/alpha)+tan^(-1)((alpha+1)/alpha)` is equal to

A

`pi`

B

`(5pi)/4`

C

`(3pi)/4`

D

`(3pi)/2`

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