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

Multiple Choice

Find all points (x, y) where $f ( x , y ) = x ^ { 2 } + x y + y ^ { 2 } - 3 x + 2$ 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) (2, -1) is a relative maximum
B) (2, -1) is a relative minimum
C) (-2, 1) is a relative maximum
D) (-2, 1) is a relative minimum