Whoops, wrong number of dimensions there. Hang on.
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!
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.
Perhaps it's simplistic, but I would evaluate 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.