Question

find the average rate of change of the function f(x)=8x from x_1 = 0 to x_2 = 9.
the average rate of change is . (simplify your answer.)

Explanation:

Step1: Recall the formula

The average rate of change of a function $y = f(x)$ from $x_1$ to $x_2$ is $\frac{f(x_2)-f(x_1)}{x_2 - x_1}$.

Step2: Calculate $f(x_1)$ and $f(x_2)$

Given $f(x)=8x$, when $x_1 = 0$, $f(x_1)=8\times0 = 0$; when $x_2=9$, $f(x_2)=8\times9 = 72$.

Step3: Substitute values into formula

$\frac{f(x_2)-f(x_1)}{x_2 - x_1}=\frac{72 - 0}{9-0}=\frac{72}{9}=8$.

Answer:

8