Determine the Local Extrema of the Function $f(x, y)=x^{3}+y^{3}-9 x y$

Multiple Choice

Determine the local extrema of the function.
- $f(x, y) =x^{3}+y^{3}-9 x y$

A) $f(2,2) =-20$ , minimum
B) $f(1,1) =-7$ , minimum
C) $f(3,3) =-27$ , minimum
D) no local extrema