Find the Absolute Maximum and Minimum Value Of $f ( x , y ) = x ^ { 2 } - 3 y ^ { 2 } - 2 x + 6 y$

Essay

Find the absolute maximum and minimum value of $f ( x , y ) = x ^ { 2 } - 3 y ^ { 2 } - 2 x + 6 y$ on the square region $D$ with vertices $( 0,0 )$ , $( 0,2 )$ , $( 2,2 )$ , and $( 2,0 )$ .