The absolute extrema of a function on a given domain set D are the greatest and least values of the function on D. The Extreme Value Theorem

guarantees that a continuous function must have absolute extrema on a bounded, closed interval. You can use the Closed Interval Method to locate the absolute extrema.

When can absolute extrema occur?

In this example we saw that absolute extrema can and will occur at both endpoints and critical points. One of the biggest mistakes that students make with these problems is to forget to check the endpoints of the interval.

Where do the absolute extreme values of the function occur on?

From Note, the absolute extrema must occur at endpoints or critical points. Therefore, the largest of these values is the absolute maximum of f. The smallest of these values is the absolute minimum of f.