Hi, I can't figure out the answer to this question:

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

(A) f has all of its relative extrema on the line x = y.

(B) f has all of its relative extrema on the parabola x = y2.

(C) f has a relative minimum at (0,0).

(D) f has an absolute minimum at (2/3, 2/3).

(E) f has an absolute minimum at (1, 1).

The answer is (A).

I chose (D) because point (0, 0) is a saddle point (and therefore not a relative extrema?) while point (2/3, 2/3) is indeed a minimum point. Can anyone please explain?

Much appreciated!!!

John