Chapter 2, Problem 43RE

To determine

To find: The average rate of change of the given function between $x=2$ and $x=3$ .

Answer to Problem 43RE

Average rate of change is $-5$ .

Explanation of Solution

Given:

A function is given as $f\left(x\right)=2-5x$ .

Formula used:

Average rate of change of a function $f\left(x\right)$ between $x=b$ and $x=a$ is given by

  $Avgf\left(x\right)=\frac{f\left(b\right)-f\left(a\right)}{b-a}$

Calculation:

Consider the given function.

  $f\left(x\right)=2-5x$ ................(1)

Consider the given $x$ values.

  $x=2$ and $x=3$

Now, replace $x$ by $2$ in equation (1).

  $\begin{array}{c}f\left(2\right)=2-5\left(2\right)\\ =2-10\\ =-8\end{array}$ ................(2)

Now, replace $x$ by $3$ in equation (1).

  $\begin{array}{c}f\left(2\right)=2-5\left(3\right)\\ =2-15\\ =-13\end{array}$ ................(3)

Substitute equation (2) and (3) in the formula of average rate of change and simplify as shown:

  $\begin{array}{c}Avgf\left(x\right)=\frac{f\left(b\right)-f\left(a\right)}{b-a}\\ =\frac{f\left(3\right)-f\left(2\right)}{3-2}\\ =\frac{-13+8}{1}\\ =-5\end{array}$

Hence, the average rate change of the function is $-5$ .