Question

find the average rate of change of the function $f(x)=\sqrt{x}$ from $x_1 = 9$ to $x_2 = 16$. the average rate of change is \boxed{}. (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 $x_1=9$

$f(9)=\sqrt{9}=3$

Step3: Calculate $f(x_2)$ where $x_2=16$

$f(16)=\sqrt{16}=4$

Step4: Substitute into the formula

$\frac{f(16)-f(9)}{16-9}=\frac{4-3}{16-9}=\frac{1}{7}$

Answer:

$\frac{1}{7}$