To warm up the lesson, we'll take a look at a hand-drawn continuous function over a closed interval and then find its minimum and maximum values. I wonder if we could do this kind of thing with calculus. Duration: 6:31

Here, we will formally define the absolute minimum and maximum of a function in an algebraic sense. Eventually, we want to be able to apply calculus to finding these extreme values. Duration: 6:56

After defining relative extrema, we take a look at the Extreme Value Theorem, affectionately known as the EVT. Duration: 8:04

The discoveries made in the various parts of Example 2 will lead us to discovering both the definition of critical numbers and Fermat's Theorem. Duration: 8:17

We would like to know if Fermat's Theorem works in converse. In other words, if you find a critical number for a function, does it necessarily have to be the location of a relative extremum? Example 3 will reveal the answer. Duration: 5:00