Find and Classify All Critical Points for the Function F(x

Multiple Choice

Find and classify all critical points for the function f(x, y) = 2y³ + 3y² - 12y -x² + 2x.

A) (1, -2) local maximum; (1, 1) local minimum
B) (1, -2) local maximum; (1, 1) saddle point
C) (1, -2) local maximum; (1, 1) local maximum
D) (1, -2) local minimum; (1, 1) local minimum
E) (-1, 2) saddle point; (1, 1) saddle point