Chapter 10.2, Problem 17Q

To determine

To write: The comparison between average rate of change of g to the average rate of change of $h\left(x\right)=\sqrt[3]{\frac{3}{2}x}$ over the interval $x=0$ to $x=3$ .

Answer to Problem 17Q

The average rate of change of g is $\frac{1}{0.55}$ that is, 1.8 times greater than the average rate of change of h over the interval $x=0$ to $x=3$ .

Explanation of Solution

Given information:

The graph:

  

For the average rate of change of $g\left(x\right)$ ;

From the graph write the average rate of change as:

  $\begin{array}{c}\frac{g\left(3\right)-g\left(0\right)}{3-0}=\frac{3-0}{3-0}\\ =\frac{3}{3}\\ =1\end{array}$

For the average rate of change of $h=\sqrt[3]{\frac{3}{2}x}$ ;

  $\begin{array}{c}f\left(0\right)=\sqrt[3]{\frac{3}{2}\left(0\right)}\\ =0\end{array}$

And, $\begin{array}{c}f\left(3\right)=\sqrt[3]{\frac{3}{2}\left(3\right)}\\ \approx 1.65\end{array}$

From the graph write the average rate of change as:

  $\begin{array}{c}\frac{f\left(3\right)-f\left(0\right)}{3-0}=\frac{1.65-0}{3-0}\\ \approx 0.55\end{array}$

Hence, the average rate of change of g is $\frac{1}{0.55}$ that is, 1.8 times greater than the average rate of change of h over the interval $x=0$ to $x=3$ .