Absolute Extrema

The absolute maximum of a function $f(x,y)$ on a region $R$ is $f(x_0,y_0)$ if $(x_0,y_0)\in R$ and

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

for all $(x,y)\in R$.

The absolute minimum of a function $f(x,y)$ on a region $R$ is $f(x_0,y_0)$ if $(x_0,y_0)\in R$ and

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

for all $(x,y)\in R$.