Lectures>Practice

# Maximum and Minimum Values

One of the most common and powerful applications of the derivative is finding intervals where functions are increasing versus decreasing and, by extension, where their local maximum and minimum values are.

# Videos

Our first application will be finding the maximum and minimum values of a function. Before we can do that, we need to be clear on the difference between the two types of extrema - local vs. absolute.
Now that we're clear on what we mean by the two kinds of extrema, local versus absolute, we can talk about how we can use calculus to find them.
Calling this one an "application" is a bit of a stretch. It's a really useful tool but more for proving other things than for actually answering practical questions. It's going to be an essential tool, for example, in our method for deciding where a function is increasing versus decreasing in the next section.
Another practical question we can ask is, "When is a function increasing versus decreasing?" This is a direct consequence of the idea that a positive rate of change means something is increasing where a negative rate of change means it's decreasing.
Using our new test for increasing vs. decreasing, we can now revisit the question of how can we find the local extrema of a function.
In part 1, we talked about the method and looked at a couple of basic examples. In this lecture, we're going to look at some more examples, that are a little more interesting.