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 $f_{y}(x, y) =0$ .
- $f(x, y) =x^{2}+x y+y^{2}+2 x+3 y$

A) $\mathrm{x}=\frac{1}{3}, \mathrm{y}=\frac{4}{3}$
B) $\mathrm{x}=-\frac{1}{3}, \mathrm{y}=-\frac{4}{3}$
C) $\mathrm{x}=-\frac{4}{3}, \mathrm{y}=-\frac{1}{3}$
D) $\mathrm{x}=\frac{4}{3}, \mathrm{y}=\frac{1}{3}$