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Let F:RtoR be a thrice differntiable fun...

Let `F:RtoR` be a thrice differntiable function. Suppose that `F(1)=0,F(3)=-4` and `F'(x)lt0` for all `x epsilon(1//2,3)`. Let `f(x)=xF(x)` for all `x inR`. Then the correct statement(s) is (are)

A

`f'(1)lt0`

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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