Answer
The average rate of change of $f\left( x \right)=\sqrt{x}$ from ${{x}_{1}}=4$ to ${{x}_{2}}=9$ is $\underline{\frac{1}{5}}$.
Work Step by Step
The average rate of change:
$\begin{align}
& r=\frac{f\left( 9 \right)-f\left( 4 \right)}{9-4} \\
& =\frac{\sqrt{9}-\sqrt{4}}{9-4} \\
& =\frac{3-2}{5} \\
& =\frac{1}{5}
\end{align}$
Therefore, the average rate of change is $\frac{1}{5}$.
