## Introduction to Derivatives

Read this section to lay the groundwork for introducing the concept of a derivative. Work through practice problems 1-5.

##### PREVIEW OF CHAPTER 3

The two previous chapters have laid the foundation for the study of calculus. They provided a review of some material you will need, and they started to emphasize the various ways we will need to view and use functions: functions given by graphs, equations, and tables of values.

Chapter 2 will focus on the idea of tangent lines. We will get a definition for the derivative of a function and calculate the derivatives of some functions using this definition. Then we will examine some of the properties of derivatives, see some relatively easy ways to calculate the derivatives, and begin to look at some ways we can use derivatives. Chapter 2 will emphasize what derivatives are, how to calculate them, and some of their applications.

This section begins with a very graphical approach to slopes of tangent lines. It then examines the problem of finding the slopes of the tangent lines for a single function, $y = x^2$ , in some detail, and illustrates how these slopes can help us solve fairly sophisticated problems.