Examine the Function $f ( x , y ) = 4 x ^ { 2 } - 2 x y + 4 y ^ { 2 } + 120 x + 60 y$

Multiple Choice

Examine the function $f ( x , y ) = 4 x ^ { 2 } - 2 x y + 4 y ^ { 2 } + 120 x + 60 y$ for relative extrema.

A) relative $\text { minimum }$ at $( - 18 , - 12 )$
B) relative $\text { maximum }$ at $( - 18 , - 12 )$
C) relative $\text { minimum }$ at $( - 18,12 )$
D) relative $\text { maximum }$ at $( - 18,12 )$
E) no relative extrema