Finding extrema (minima and maxima) of a function

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• June 8th 2010, 11:31 AM
Iukwim
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!
• June 8th 2010, 11:34 AM
Ackbeet
Whoops, wrong number of dimensions there. Hang on.
• June 8th 2010, 11:39 AM
Iukwim
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.
• June 8th 2010, 11:41 AM
Ackbeet
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.