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Let S be the set of all twice differenti...

Let S be the set of all twice differentiable functions f from `RR` to `RR` such that `(d^2 f)/(dx^2)(x) gt 0` for all `x in (-1,1)`. For `f in S`, let `X_f` be the number of points `x in (-1,1)` for which `f(x)=x`. Then which of the following statements is(are) true?

A

There exists a function `f in S` such that `X_f=0`

B

For every function `f in S`, we have `X_f le 2`

C

There exists a function `f in S` such that `X_f =2`

D

There does NOT exist any function f in S such that `X_f =1`

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