1.3 Rates of Change in Linear and Quadratic Functions

In Unit 1.3 of AP Precalculus, you expand your analysis of rates of change to polynomial functions of degree greater then or equal to 3. Unlike linear functions (where the rate of change is constant) or quadratic functions (where the rate of change changes at a constant rate), higher-degree polynomial functions have rates of change that alternate between increasing and decreasing over different intervals. The points where a polynomial function changes from increasing to decreasing (or vice versa) are called local extrema (local maximums and local minimums). Between these points, you analyze the rate of change over an interval [a,b] using: