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}
$