Relative Extrema

A function $f(x,y)$ is said to have a relative minimum $f(x_0,y_0)$ at a point $(x_0,y_0)$ in its domain if there exists a circle in the $xy$-plane centered at $(x_0,y_0)$ such that for all points $(x,y)$ inside the circle

$$f(x,y)\le f(x_0,y_0)$$

A function $f(x,y)$ is said to have a relative maximum $f(x_0,y_0)$ at a point $(x_0,y_0)$ in its domain if there exists a circle in the $xy$-plane centered at $(x_0,y_0)$ such that for all points $(x,y)$ inside the circle

$$f(x,y)\ge f(x_0,y_0)$$