Suppose That $f ( x , y ) = x ^ { 2 } + 3 x y + y ^ { 2 }$

Multiple Choice

Suppose that $f ( x , y ) = x ^ { 2 } + 3 x y + y ^ { 2 }$ Find an equation of the tangent plane to the graph of f at the point (2, 2) .

A) $z = 20 + 10 ( x - 2 ) + 10 ( y - 2 )$
B) $z = 20 - 10 ( x - 2 ) - 10 ( y - 2 )$
C) $z = 20 - 10 ( x - 2 ) + 10 ( y - 2 )$
D) $z = 20 + 10 x + 10 y$