I'm having some real difficulty classifying the critical points for the following function (sorry LaTex doesn't seem to want to work)

g(x,y)=x^(3)-3xy^(2)+y^(4)

Could someone help me, i've found the critical points to be (0,0) (3/2,3/2) and (3/2, -3/2)

But for (0,0) I find the second derivative test is inconclusive (because g11g22-g12^2=0) equal 0)