# Critical points

pbialos
Given $$n\geq 2, n\in \aleph$$ and $$f(x,y)=a*x^n+c*y^n$$ where $$a*c\not=0$$, determine the nature of the critical points. I found the only critical point at (0,0) and when i tried to use the criteria of the determinant of the hessian matrix to determine the kind of critical point it was, it gave me 0, so i can`t say nothing by this criteria.
I dont know what kind of analysis of the function i am supposed to do, so any help would be much appreciated.

Many Thanks, Paul.

AKG