I have many functions with two variables $x$ and $y$, for which I need to compute min and max to see if they are in the range I want them to be. For example:
$$z = 0.5 - 0.25 \cos(\pi x) - 0.25 \cos(\pi y),$$ where $x\in[0,1]$ and $y\in[0,1]$.
I tried Wolfram Alpha but for some reason it does not compute the min and max.
Thanks
For minimum, make $\cos \pi x$, $\cos\pi y$ as big as possible. That happens at $x=y=0$.
For maximum, make $\cos \pi x$, $\cos\pi y$ as small (big negative) as possible. That happens when $x=y=1$, since $\cos \pi=-1$.
Remark: For the other functions you are concerned about, one cannot make suggestions without at least seeing some examples. For the class of functions you are considering, there may be a simple general procedure. If the class is fairly general, we may need tools from the calculus. However, I would expect that Wolfram Alpha can usually handle such problems.