what is the average rate of change of f(x) from x1 = 2 to x2 = 4? please write your answer rounded to the…

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 $f(x_1)$

Given $f(x)=\sqrt{3x + 1}$ and $x_1 = 2$, then $f(2)=\sqrt{3\times2+1}=\sqrt{6 + 1}=\sqrt{7}$.

Step3: Calculate $f(x_2)$

Given $x_2 = 4$, then $f(4)=\sqrt{3\times4+1}=\sqrt{12 + 1}=\sqrt{13}$.

Step4: Calculate the average rate of change

The average rate of change is $\frac{f(4)-f(2)}{4 - 2}=\frac{\sqrt{13}-\sqrt{7}}{2}$. Using a calculator, $\sqrt{13}\approx3.606$, $\sqrt{7}\approx2.646$. Then $\frac{3.606 - 2.646}{2}=\frac{0.96}{2}=0.48$.

Answer:

$0.48$