For a real function $f$ prove that there exists a point $a$

Home Forums Math Olympiad, I.S.I., C.M.I. Entrance For a real function $f$ prove that there exists a point $a$

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    Soham Chatterjee
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    Let $f$ be a real function on the real line with continuous third derivative. Prove that there exists a point $a$ such that $$f(a)\cdot f^{\prime}(a)\cdot f^{\prime \prime}(a)\cdot f^{\prime \prime \prime}(a)\geq 0$$

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