Finding system of equations from critical points

Question

We've gotten a function $f(x,y)=3x^3+3x^2y-y^3-15x$. For this function, it is told that the critical points of $f$ is $A = (1,1), B = (-1,-1),C = (\sqrt5,-\sqrt5), D = (-\sqrt5, \sqrt 5)$. These are the solutions to a system of two equations, and I can't seem to find any information on how to find these two equations? Note that it is not required to solve the equations, just find them.

Thanks in advance.

Answer 1

The two equations are

$f_x(x,y)=0$ and $f_y(x,y)=0.$