College Algebra, Chapter 3, 3.4, Section 3.4, Problem 14

A function $\displaystyle f(x) = x + x^4$. Determine the average rate of change of the function between $x = -2$ and $x = 3$.


$\begin{equation} \begin{aligned} \text{average rate of change } =& \frac{f(b) - f(a)}{b - a} && \text{Model} \\ \\ \text{average rate of change } =& \frac{f(3) - f(-1)}{3 - (-1)} && \text{Substitute } a = -1 \text{ and } b = 3 \\ \\ \text{average rate of change } =& \frac{3 + (3)^4 - [-1 + (-1)^4]}{3 + 1} && \text{Simplify} \\ \\ \text{average rate of change } =& \frac{3 + 81}{4} && \text{Combine like terms} \\ \\ \text{average rate of change } =& \frac{84}{4} && \text{Reduce to lowest terms} \\ \\ \text{average rate of change } =& 21 && \text{Answer} \end{aligned} \end{equation}$