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Let F : R to R be a thrice differentia...

Let F : R `to` R be a thrice differentiable function . Suppose that `F(1)=0,F(3)=-4 and F(x) lt 0 " for all" x in (1,3), f(x) = x F(x) `for all `x inR`.
The correct statement (s) is / are

A

`f'(1) lt 0`

B

`f (2) lt 0`

C

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

D

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

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The correct Answer is:
A, B, C
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