Find Values Of $x$ And $y$ Such That Both $f_{x}(x, y)=0$ And $f_{y}(x, y)=0$

Multiple Choice

Find values of $x$ and $y$ such that both $f_{x}(x, y) =0$ and $f_{y}(x, y) =0$ .
- $f(x, y) =3 x^{2}+12 x y+y^{2}$

A) $x=0, y=0$
B) $x=-4, y=-4$
C) $x=0, y=-4$
D) $x=-4, y=0$