Question

Let f(x,y)=x^2-2xy+y^3 Which of the following is true?

Answer 1

f has all of its relative extrema on the line x=y
f has all of its relative extrema on the parabola x=y^2
f has a relative minimum at (0,0)
fhas an absolute minimum at (2/3,2/3)
f has an absolute minimum at (1,1)

Answer 2

I guess I'm looking for tricks of how to do this fast as possible.

Answer 3

how about something like this