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Math Help - A proof about maximum point, critical point and differentiation

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    A proof about maximum point, critical point and differentiation

    Let E\subset \mathbb{R}^n and f: E\rightarrow\mathbb{R} be a continuous function. Prove that if ais a local maximum point for f, then either f is differentiable at x = a and Df(a) = 0 or f is not differentiable at x = a. Deduce that if f is differentiable on E^o, then a global maximum point of f is either a critical point of f or an element of \partial     E.








    It's a little bit about optimization but stil analysis. Well I have no idea about this question and I think I need a proof. Thank you!
    Last edited by ianchenmu; March 4th 2013 at 09:18 PM.
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