Question

find and classify the relative extrema of h(x,y)=x^3+2xy^2+3x^2+2y^2+4.

Answer 1

I found critical points:
\[(-1,\pm \sqrt{3/2}\]),
(0,0) and (-2,0). When I checked D\[(-1,\pm\sqrt{3/2}\]) it came out to be less than zero while fxx=0. Does this just mean the test is inconclusive?

Answer 2

D<0 means saddle point

Answer 3

when D=0 the test is inconclusive

Answer 4

Oh shoot, right. Thanks Zarkon. I saw the fxx=0 and completely forgot about that.