Let (x, y) = y 2 x yx 2 + xy. (a) Show that the critical points (x, y) satisfy the equations y(y -

Let ƒ(x, y) = y²x − yx² + xy.

(a) Show that the critical points (x, y) satisfy the equations y(y - 2x + 1) = 0, x(2y-x + 1) = 0 (b) Show that f has three critical points where x = 0 or y = 0 (or both) and one critical point where x and y are nonzero. (c) Use the Second Derivative Test to determine the nature of the critical points.