I need to find the maximum and minimum of functions in space. I've managed to solve a few exercises, but for some of them I get stuck when trying to solve for x and y. I'll give two examples below, hoping someone can point out what I'm doing wrong.

First example:

I approach this problem like this.

Find the points at the end (not sure what these are called in English?). They are

(0,0), (1,0), (0,1).

Find the maximum and minimum points inside the area. We find these by deriving the function twice; once with regards to x, once with regards to y. We then need find where they are zero.

This is where I get stuck. How to proceed from here, assuming I've done right so far?

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