I've got the next function: $f(x,y)=x^3y^3$ where $x,y\in \mathbb R$
I need to determine whether there is minima, maxima or saddle point.
Easily enough, after doing the partial derivatives
I get the point $(0,0)$.
Now, how can i "officially" prove that that point isn't a minima, maxima or saddle point? Is it enough to show that hessian matrix gives 0? Do i need to show that the function can get higher [/lower] values using other points on the function?