Definition:Maximum Value of Real Function/Absolute

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.

Also see

 * Definition:Local Maximum


 * Definition:Absolute Minimum
 * Definition:Local Minimum