find the average rate of change of f(x) = 11/x over the interval 8, 10. 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, $a = 8$, $b = 10$, and $f(x)=\frac{11}{x}$.

Step2: Calculate $f(10)$ and $f(8)$

$f(10)=\frac{11}{10}$ and $f(8)=\frac{11}{8}$.

Step3: Substitute into the formula

$\frac{f(10)-f(8)}{10 - 8}=\frac{\frac{11}{10}-\frac{11}{8}}{2}$. First, find a common denominator for $\frac{11}{10}-\frac{11}{8}$. The common denominator of 10 and 8 is 40. So $\frac{11}{10}-\frac{11}{8}=\frac{11\times4}{10\times4}-\frac{11\times5}{8\times5}=\frac{44}{40}-\frac{55}{40}=-\frac{11}{40}$. Then $\frac{-\frac{11}{40}}{2}=-\frac{11}{40}\times\frac{1}{2}=-\frac{11}{80}=- 0.1375$. Rounding to the nearest tenth gives $-0.1$.

Answer:

$-0.1$