Locate and Classify All Critical Points for the Given Function $f(x, y)=x^{3}-5 x y+y^{3}$

Multiple Choice

Locate and classify all critical points for the given function.
- $f(x, y) =x^{3}-5 x y+y^{3}$
Only find the critical points for this function.
Do not test for maximum or minimum.

A) $(0,0)$
B) $\left(\frac{5}{3}, \frac{5}{3}\right)$
C) $(0,0)$ and $\left(\frac{5}{3}, \frac{5}{3}\right)$
D) There are no critical points.