Find All Points (X, Y) Where $f ( x , y ) = x ^ { 3 } - 12 y + y ^ { 2 }$

Multiple Choice

Find all points (x, y) where $f ( x , y ) = x ^ { 3 } - 12 y + y ^ { 2 }$ has a possible relative maximum or minimum. Use the second-derivative test to determine, if possible, the nature of f(x, y) at each of these points.

A) Test Inconclusive
B) (0, 6) gives a relative maximum
C) (0, 0) gives a relative minimum
D) (0, 0) gives a relative maximum