Question

I'm wondering about critical points on a function in two variables. They say it's enough that the partial derivatives in the x and y-direction are zero. I can't help thinking though about all the other directions there are... Why is it enough to only bother looking at the x- and y-direction?

Answer 1

When the x- and y-partial derivatives are zero you get two equations which you solve simultaneously, i.e. you don't look for the critical points only in x- or y-directions, you look them in both directions simultaneously.

Answer 2

i think it gives you a plane that is the slope