f(x) is a differentiable function and g(x) is a double differentiabl – InterviewSolution

1.	f(x) is a differentiable function and g(x) is a double differentiable function such that \|f(x)\|≤1 and f'(x)=g(x) . If f2(0)+g2(0)=9 . Prove that there exists some c∈(–3,3) such that g(c).g''(c)
Answer» f(x) is a differentiable function and g(x) is a double differentiable function such that \|f(x)\|≤1 and f'(x)=g(x) . If f2(0)+g2(0)=9 . Prove that there exists some c∈(–3,3) such that g(c).g''(c)<0.

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