2.1: The Slope of a Function
In this subunit, you will look at the first of two major problems that lie at the heart of calculus: the tangent line problem. This intellectual exercise demonstrates the origins of derivatives for nonlinear functions.
Read Section 2.1 (pages 29-33). You will be introduced to the notion of a derivative through studying a specific example. The example will also reveal the necessity of having a precise definition for the limit of a function.
Watch this video. In this lecture, Jerison introduces the notion of a derivative as the rate of change of a function, or the slope of the tangent line to a function at a point.
Work through problems 1-6 for Exercise 2.1. When you are done, check your answers against Appendix A.