Question

find the average rate of change of the function f(x) = √x from x₁ = 100 to x₂ = 144. the average rate of change is . (simplify your answer.)

Explanation:

Step1: Recall the 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 $f(x)=\sqrt{x}$, when $x_1 = 100$, $f(x_1)=\sqrt{100}=10$; when $x_2 = 144$, $f(x_2)=\sqrt{144}=12$.

Step3: Substitute values into the formula

$\frac{f(x_2)-f(x_1)}{x_2 - x_1}=\frac{12 - 10}{144-100}=\frac{2}{44}=\frac{1}{22}$.

Answer:

$\frac{1}{22}$