Suppose that f(x, y) = x²y²kxy. Find and classify the critical points, and discuss how they change when k takes on different values.
A) The critical points are (0, 0) and (1/k, 1/k). They remain the same regardless of the value of k.
B) The critical points are (0, 0) and (1/k, 1/k). They shift horizontally as k changes.
C) The critical points are (0, 0) and (-1/k, -1/k). They shift vertically as k changes.
D) The critical points are (0, 0) and (-1/k, -1/k). They remain the same regardless of the value of k.