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Let F:R- R be a thrice differentiable fu...

Let `F:R- R` be a thrice differentiable function. Suppose that `F(1)=0,F(3)=-4` and `F(x)<0` for all `x in (1/2,3)`. Let `f(x)=xF(x)` for all `x in R` The correct statement is

A

`f'(1) lt 0`

B

`f(2) lt 0`

C

`f'(x) ne 0` for any `x in (1,3)`

D

`f'(x) = 0` for some `x in (1,3)`

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The correct Answer is:
ABC
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