Question

find the average rate of change of the function f(x)=8x from x₁=0 to x₂=4. the average rate of change is \square. (simplify your answer.)

Explanation:

Step1: Recall average rate formula

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

Step2: Calculate $f(x_1)$ where $x_1=0$

$f(0)=8\times0=0$

Step3: Calculate $f(x_2)$ where $x_2=4$

$f(4)=8\times4=32$

Step4: Substitute into the formula

$\frac{f(4)-f(0)}{4-0}=\frac{32-0}{4-0}$

Step5: Simplify the expression

$\frac{32}{4}=8$

Answer:

8