The Absolute Minimum Of $f ( x , y ) = 2 x ^ { 2 } + y ^ { 2 } - 4 x - 4 y + 1$

Multiple Choice

The absolute minimum of $f ( x , y ) = 2 x ^ { 2 } + y ^ { 2 } - 4 x - 4 y + 1$ on or inside the triangle with vertices (0,0) , (1,2) , and (0,2) is

A) 1137
B) -61
C) -5
D) 4
E) 1