Let (x, y) = y 2 - 2x 2 y + 4x 3 + 20x 2 .

Let ƒ(x, y) = y² - 2x²y + 4x³ + 20x². The only critical points are (-2, 42, 10, 0), and (5, 25). Which of the following correctly describes the behavior of ƒ at these points?

(a) (-2, 4): local (relative) minimum
(0, 0): local (relative) minimum
(5, 25): local (relative) maximum

(b) (-2, 4): local (relative) minimum
(0, 0): local (relative) maximum
(5, 25): local (relative) maximum

(c) (-2, 4): neither a local (relative) minimum nor a local (relative) maximum
(0, 0): local (relative) maximum
(5, 25): local (relative) minimum

(d) (-2, 4): local (relative) maximum
(0, 0): neither a local (relative) minimum nor a local (relative) maximum
(5, 25): local (relative) minimum

(e) (-2, 4): neither a local (relative) minimum nor a local (relative) maximum
(0, 0): local (relative) minimum
(5, 25): neither a local (relative) minimum nor a local (relative) maximum