---
tag: 0WFBH1Q3WC
kind: concept
name: Local maximum and minimum
aliases: [local-extremum, relative-extremum]
msc: [26B99]
uses: [0JPCHTXWG0]
sources:
  - url: https://en.wikipedia.org/wiki/Maximum_and_minimum
    locator: Definition
---

## Summary

A [[function of several real variables|0JPCHTXWG0]] has a local maximum at a point when no nearby point of the domain gives a larger value.
It has a local minimum when no nearby point gives a smaller value, and a local extremum is either of the two.