By examining the behavior of x^3 - 3xy^2 on straight lines through the origin, show that the surface z = x^3 - 3xy^2 qualifies as a monkey saddle?
Can someone explain how I would go about doing this problem? I'm very confused
You should read this page, it is very inspiring as to what the surface looks like and why; the discussion after $\displaystyle z(x,y)={\rm Re}(x+iy)^3$ answers exactly your question, in slightly different terms.