The behavior of a function can be complicated near a critical point where D=0. Suppose that f(x,y)= x^3 - 3xy^2.
a.) Show that there is one critical point at (0,0) and that D=0 at that point.
b.) Show that the contour for f(x,y)=0 consists of three lines intersecting at the origin where f alternates from positive to negative. Sketch a contour diagram for f near 0.
I already did part a, but I have no idea how to even start part b.