\( f: R \rightarrow R, f(x) \) is a differentiable function such that all its successive derivat...

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\( f: R \rightarrow R, f(x) \) is a differentiable function such that all its successive derivatives exist. \( f^{\prime}(x) \) can be zero at discrete points only and \( f(x) \cdot f^{\prime \prime}(x) \leq 0 \forall x \in R \).
If \( f(a)=0 \), then which of the following is correct
(a) \( f(a+h) f^{\prime \prime}(a-h)0 \)
(b) \( f(a+h) f^{\prime \prime}(a-h)0 \)
(c) \( f^{\prime}(a+h) f^{\prime \prime}(a-h)0 \)
(d) \( f^{\prime}(a+h) f^{\prime \prime}(a-h)0 \)
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