For $f ( x , y )$ , Find All Values of X and Y Such That

Multiple Choice

For $f ( x , y )$ , find all values of x and y such that $f _ { x } ( x , y ) = 0$ and $f _ { y } ( x , y ) = 0$ simultaneously. $f ( x , y ) = 16 x ^ { 3 } - 4 x y + 16 y ^ { 3 }$

A) $\left( - \frac { 1 } { 12 } , - \frac { 1 } { 12 } \right)$
B) $\left( \frac { 1 } { 12 } , \frac { 1 } { 12 } \right)$
C) (0,0)
D) Both B and C
E) Both A and B