Question

question 20 (1 point) find the average rate of change of the function from x1 to x2. f(x) = √(2x) from x1 = 2 to x2 = 8 a) 2 b) 1/3 c) 7 d) - 3/10

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 $f(x)=\sqrt{2x}$, when $x_1 = 2$, $f(x_1)=\sqrt{2\times2}=\sqrt{4}=2$. When $x_2 = 8$, $f(x_2)=\sqrt{2\times8}=\sqrt{16}=4$.

Step3: Substitute values into formula

$\frac{f(x_2)-f(x_1)}{x_2 - x_1}=\frac{4 - 2}{8 - 2}=\frac{2}{6}=\frac{1}{3}$.

Answer:

B. $\frac{1}{3}$