Critical Point

A point $(x_0,y_0)$ in the domain of a function $f(x,y)$ is said to be a critical point of $f(x,y)$ if

$$\frac{\partial f}{\partial x}{|}_{(x_0,y_0)}=0,\text{and }\frac{\partial f}{\partial y}{|}_{(x_0,y_0)}=0$$

or if one of the above does not exist at $(x_0,y_0)$

This can be extended to higher dimensions as:

$$\nabla f{|}_P=\vec{0}$$