Examples of Extrema

mountain peaks are local extrema of altitude

We encounter extrema on a day to day basis. Here is just a small collection of examples:

The highest point in a given region.
The fastest runner in a given race.
The shortest distance between two objects.
The lowest temperature at a certain site during a given year.

These examples illustrate that many extremum questions can be formulated mathematically. In this section we shall learn how to use derivatives to detect extrema.

Return to the main document on extrema