Extreme Values on Closed Intervals Discussion

(The following is/are the initial prompt(s) for an online discussion; students may have posted responses, and prompts for further discussion may have been added, but these things are not shown.)

Often, extreme value problems need answers that lie in some closed interval. You can solve such problems similarly, but not identically, to how you solve extreme value problems for open or unbounded intervals. “Locating Absolute Extrema” in section 4.3 of our textbook discusses the process. This discussion is intended to help make it concrete for you.

To begin, how would you describe, in your own words, the process for finding extreme values on a closed interval, and its similarities to and differences from the process for finding them on open or unbounded intervals?