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I would appreciate any assistance with the following question: Suppose f \in C^2[-1,1] is twice continuously differentiable. Prove that

|f'(0)|^2 \leq 4 ||f||_\infty (||f||_\infty + ||f''||_\infty), where ||f||_infty is the standard sup norm. At first I thought Taylor expansion seemed promising, but I am pretty stymied.

Thank you!

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# Bounding the L-Infty Norm of a Diffble Fn

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