Question

A. Find the critical points.

B. Use the second derivative test to

classify each critical point.

f (x, y) = −x^3 + 9xy − y^3

A.

A. (1,1)and(0,0)

B. (3,3)and(0,0)

C. (1, 1) only
D. (-3, -3) and (0, 0)

E. (-3, -3) only

F. not listed

B. Which are true?

A. The critical points generate one relative maximum and one relative minimum. B. The critical points generate one relative maximum and one saddle point.

C. The critical points generate one relative minimum.
D. The critical points generate one relative minimum and one saddle point.

E. The second derivative test was inconclusive about all critical points.
F. None of the statements is true.