An absolute maximum is a point on a curve or surface where the value of the function is greater than all other points. In other words, it is the highest point on the entire curve or surface.

This can be described formally by saying there exists an absolute maximum of the function at if for all in the domain of .

Example

Finding Absolute Maximum

If a function is continuous over a closed interval, then there exists an absolute maximum within that interval. To find the absolute maximum check all the critical point within the interval and both the endpoints of the interval.

Example

Given the function find the absolute maximum over the interval .

There exists an absolute maximum over the interval for the function . of at .