find the average rate of change of f(x) = 4√x over the interval 17, 18. write your answer as an integer…

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = f(x)$ over the interval $[a,b]$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a = 17$, $b = 18$, and $f(x)=4\sqrt{x}$.

Step2: Calculate $f(18)$ and $f(17)$

$f(18)=4\sqrt{18}=4\sqrt{9\times2}=4\times3\sqrt{2}=12\sqrt{2}$, $f(17)=4\sqrt{17}$.

Step3: Substitute into the formula

$\frac{f(18)-f(17)}{18 - 17}=\frac{12\sqrt{2}-4\sqrt{17}}{1}=12\sqrt{2}-4\sqrt{17}$. Now, $12\sqrt{2}\approx12\times1.414 = 16.968$ and $4\sqrt{17}\approx4\times4.123=16.492$. Then $12\sqrt{2}-4\sqrt{17}\approx16.968 - 16.492=0.476\approx0.5$.

Answer:

$0.5$