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Math Help - Differentiable function

  1. #1
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    Differentiable function

    Suppose f(x) is a diferentiable function and g(x) is a doubly differentiable function such that f'(x)=g(x) and |f(x)| \leq 1 and |g(x)| \geq 2 for all x \in [-3,3]. If further [f(0)]^{2}+[g(0)]^{2}=9, prove that there exists some c \in (-3,3) such that g(c) \cdot g''(c)<0.
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  2. #2
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    Sorry a Mistake

    There is no condition on g as |g(x)|>2.
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