The Absolute Minimum Of $f ( x , y ) = 2 x + 2 y - x ^ { 2 } - y ^ { 2 } + 2$

Multiple Choice

The absolute minimum of $f ( x , y ) = 2 x + 2 y - x ^ { 2 } - y ^ { 2 } + 2$ on or inside the triangle with vertices (0, 0) , (9, 0) , and (0,9) is

A) -69
B) -61
C) -56
D) -51
E) -47