absolute extremum

The single largest or smallest value a function attains over its entire domain (or a given interval).

An absolute maximum (minimum) of $f$ on a set $S$ is a value $f(c)$ with $f(c)\ge f(x)$ ( $f(c)\le f(x)$ ) for every $x$ in $S$ . The Extreme Value Theorem guarantees both exist for a continuous function on a closed, bounded interval.

Examples

On $[0,3]$ , $f(x)=x^2$ has absolute minimum $0$ at $x=0$ and absolute maximum $9$ at $x=3$ .