ABSTRACT
Fixed points and cycles are among the most important kinds of orbits of a dynamical system, so it is important that people be able to find them easily. As they have seen, sometimes this involves solving equations or drawing accurate graphs. One of the simplest criteria for finding fixed points is an immediate consequence of the following important fact from calculus: the intermediate value theorem and fixed point theorem. There are two markedly different types of fixed points, attracting and repelling fixed points. The importance of the Mean Value Theorem lies in its two corollaries: attracting fixed point theorem and repelling fixed point theorem. Just as in the case of fixed points, periodic points may also be classified as attracting, repelling, or neutral. This chapter provides an example to investigate how quickly an orbit is attracted to a fixed point.
