Determine the Local Extrema of the Function $f(x, y)=4 x y-x^{2} y-x y^{2}$

Multiple Choice

Determine the local extrema of the function.
- $f(x, y) =4 x y-x^{2} y-x y^{2}$

A) none
B) $\left\{\left(\frac{4}{3}, \frac{4}{3}\right) =2.37\right.$ , maximum
C) $\mathrm{f}(0,0) =0$ , minimum
D) $\left\{\left(\frac{2}{3}, \frac{2}{3}\right) =1.185\right.$ , maximum