I'm having some trouble classifying critical points when the 2nd derivative test fails.
The function is,
The only critical point I've found is (0,0).
The second derivative test fails for this point, so I've got to classify it another way.
I can try to get a rough idea of what the surface looks like by drawing cross sections, and maybe I can get a good enough picture to classify my point.
z = y^4
Z = x^4
So at the bottom sits my critical point and I have to parabolas in the y-z plane and x-z plane.
This makes me think my point may be a relative min.
How can I figure out whether all values of Z are positive or not?