Question: Undefined Hessian

HI to all!

I've a math question about the Hessian Matrix. I know that it's used for clasify critical points of a 3-D function, but what happens if the Hessian is undefined (Hessian = 0) in a point?... How i can analyze the critical point?...

A particular sample is:  f(x,y) = (y-x)^2*(y+x).

The gradient vector of this function is: grad(f)= [ 3x^2 - 2xy - y^2 , -x^2 - 2xy + 3y^2 ]. To find critical points we have to do grad(f)=0 (vector). And in this case it's easy to verify that the critical points lie in the Y=X line.

In this case the analysis of the Determinant of the Hessian Matrix (Fxx*Fyy-Fxy^2) gives 0 for the points of this line. So how can I continue the analysis, without using maple?. Is there a method for analizing these special cases?

Thanks in Advance!

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