At least on this one you have made an effort! The whole point of taking partial derivatives is that the critical points occur where the derivatives are 0!

Solve \(\displaystyle 1- e^x= 0\) and 2y= 0.

I know I'm supposed to use this rule:

d=fxxfyy-(fxy)^2

If d>0:
fxx(a,b)>0, then f(a, b) is a rel min
fxx(a,b)<0, then f(a,b) is a rel. max

At least on this one you have made an effort! The whole point of taking partial derivatives is that the critical points occur where the derivatives are 0!