Use Taylor's Formula to Find the Requested Approximation of F(x $f ( x , y ) = \frac { 1 } { ( 1 + x + 6 y ) ^ { 2 } }$

Multiple Choice

Use Taylor's formula to find the requested approximation of f(x, y) near the origin.
-Quadratic approximation to $f ( x , y ) = \frac { 1 } { ( 1 + x + 6 y ) ^ { 2 } }$

A) $1 + 2 x + 12 y + 3 x ^ { 2 } + 36 x y + 108 y ^ { 2 }$
B) $1 + 2 x + 12 y + 3 x ^ { 2 } - 36 x y + 108 y ^ { 2 }$
C) $1 - 2 x - 12 y + 3 x ^ { 2 } + 36 x y + 108 y ^ { 2 }$
D) $1 - 2 x - 12 y + 3 x ^ { 2 } - 36 x y + 108 y ^ { 2 }$