Local Maxima and Minima

Guided Notes for this lecture

Now that we have the formulas to more easily compute derivatives, we can now use those to find local maximum and minima of various functions.

Finding critical points of various functions requires different types of algebra. Let's practice some advanced examples.

Once we have our critical points we need to determine if they are local max's or min's. We begin by determining how to classify critical points if we have the original function.

At times we may only have access or information about the first derivative function. We will learn how we can use the first derivative function to classify our critical points. .

Let's consider some advanced examples using the first derivative.

Sometimes we only have access or information to the second derivative of a function. Here we will learn how to use the second derivative to classify critical points.

Now let's consider some advanced examples using the second derivative.

At the end of this section you should be able to answer the following questions:

1. What information do we need to determine critical points for a function?
2. How do we determine which test to use to classify our critical points?
3. How can we check if our solution about local max's and min's are correct?

Check Your Understanding
You should try these problems before reviewing the solutions to to these non-graded practice problems.