Sunday, April 27, 2008

Applications of Derivatives - Part 1

Good online material

List of the topics

Rates of Change The point of this section is to remind us of the application/interpretation of derivatives that we were dealing with in the previous chapter. Namely, rates of change.

Critical Points In this section we will define critical points. Critical points will show up in many of the sections in this chapter so it will be important to understand them.

Minimum and Maximum Values In this section we will take a look at some of the basic definitions and facts involving minimum and maximum values of functions.

Finding Absolute Extrema Here is the first application of derivatives that we’ll look at in this chapter. We will be determining the largest and smallest value of a function on an interval.

The Shape of a Graph, Part I We will start looking at the information that the first derivatives can tell us about the graph of a function. We will be looking at increasing/decreasing functions as well as the First Derivative Test.

The Shape of a Graph, Part II In this section we will look at the information about the graph of a function that the second derivatives can tell us. We will look at inflection points, concavity, and the Second Derivative Test.

The Mean Value Theorem Here we will take a look that the Mean Value Theorem.

Optimization Problems This is the second major application of derivatives in this chapter. In this section we will look at optimizing a function, possible subject to some constraint.

More Optimization Problems Here are even more optimization problems.

L’Hospital’s Rule and Indeterminate Forms This isn’t the first time that we’ve looked at indeterminate forms. In this section we will take a look at L’Hospital’s Rule. This rule will allow us to compute some limits that we couldn’t do until this section.

Linear Approximations Here we will use derivatives to compute a linear approximation to a function. As we will see however, we’ve actually already done this.

Differentials We will look at differentials in this section as well as an application for them.

Newton’s Method With this application of derivatives we’ll see how to approximate solutions to an equation.

Business Applications Here we will take a quick look at some applications of derivatives to the business field.

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