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Let $$F : R \rightarrow R$$ be a thrice differentiable function. Suppose that F(1) = 0, F(3) = -4 and $$F'(x) < 0$$ for all x \in $$(\frac{1}{2} , 3)$$. Let $$f(x) = xF(x)$$ for all $$x \in R$$.
The correct statement(s) is(are)
$$f'(1) < 0$$
$$f(2) < 0$$
$$f'(x) \neq 0$$ for any $$x \in (1, 3)$$
$$f'(x) = 0$$ for some $$x \in (1, 3)$$
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