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Let \( F: R \rightarrow R \) be a thrice differentiable function. Suppose that \( F(1)=0, F(3)=-4 \) and \( F^{\prime}(x)0 \) for all \( x \in(1,3) \). Let \( f(x)=x F(x) \) for all \( x \in R \).
(2015 Adv.)
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The correct statement(s) is/are
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(a) \( f^{\prime}(1)0 \)
(b) \( f(2)0 \)
(c) \( f^{\prime}(x) \neq 0 \) for any \( x \in(1,3) \) (d) \( f^{\prime}(x)=0 \) for some \( x \in(1,3) \)
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