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Math Help - Finding extrema (minima and maxima) of a function

  1. #1
    Newbie Iukwim's Avatar
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    Finding extrema (minima and maxima) of a function

    See attached file for reference, please (I translated it for you, hope you understand everything).

    I'm not sure what algorithm to use to find extrema over a closed set.
    Any help for any subsection (1-3) is much appreciated, thanks!
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  2. #2
    A Plied Mathematician
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    Whoops, wrong number of dimensions there. Hang on.
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  3. #3
    Newbie Iukwim's Avatar
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    Let me just make it clear first, that I know how to find extrema of a function of multiple variables (private derivatives etc). But my problem here is that closed set.

    Also, for the first subsection the answer that I deduce is that it has no extrema... and I think I might be wrong.
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  4. #4
    A Plied Mathematician
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    Perhaps it's simplistic, but I would evaluate f along all the boundaries, perhaps with a parametrization, and then use Calc I techniques to find the extrema along the boundaries. Compare those extrema with the ones in the interior of your region, and you should have it.
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