# Definition:Maximum Value of Real Function/Absolute

(Redirected from Definition:Maximum Value)

## Definition

Let $f: \R \to \R$ be a real function.

Let $f$ be bounded above by a supremum $B$.

It may or may not be the case that $\exists x \in \R: \map f x = B$.

If such a value exists, it is called the maximum of $f$ on $S$, and that this maximum is attained at $x$.

## Also known as

An absolute maximum is also known as a maximum value, or just a maximum if there is no need to distinguish it from a local maximum.