Find All Points (X, Y) Where F(x, Y) = $x ^ { 2 }$

Short Answer

Find all points (x, y) where f(x, y) = $x ^ { 2 }$ + xy + $y ^ { 2 }$ - x - y + 2 has a possible relative maximum or minimum.
Enter your answer exactly as just (a, b) where a, b are reduced fractions of form $\frac { \mathrm { c } } { \mathrm { d } }$ or integers.