Question

find the average rate of change of the function f(x)=2x from x_1 = 0 to x_2 = 9. the average rate of change is (simplify your answer.)

Explanation:

Step1: Recall average rate - of - change 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 $f(x)=2x$, when $x_1 = 0$, $f(x_1)=2\times0 = 0$. When $x_2 = 9$, $f(x_2)=2\times9=18$.

Step3: Substitute values into formula

Substitute $f(x_1) = 0$, $f(x_2)=18$, $x_1 = 0$, and $x_2 = 9$ into $\frac{f(x_2)-f(x_1)}{x_2 - x_1}$, we get $\frac{18 - 0}{9-0}=\frac{18}{9}=2$.

Answer:

2