Eroxl's Notes
Absolute Extrema

An absolute extremum is a point on a curve or surface that is either an absolute maximum or an absolute minimum. In other words, it is a point where the value of the function is either the maximum or minimum for the entire function. Absolute Extrema are also local extrema but all local extrema are not absolute extrema.

Example

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Finding Absolute Extrema

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 .

Finding Absolute Minimum

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

Example

Given the function find the absolute minimum over the interval .

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