Question

1. find the average rate of change of the function $h(x)=\frac{3}{x + 7}$ on the interval $1,8$.

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = h(x)$ on the interval $[a,b]$ is $\frac{h(b)-h(a)}{b - a}$. Here, $a = 1$, $b = 8$, and $h(x)=\frac{3}{x + 7}$.

Step2: Calculate $h(8)$

Substitute $x = 8$ into $h(x)$: $h(8)=\frac{3}{8 + 7}=\frac{3}{15}=\frac{1}{5}$.

Step3: Calculate $h(1)$

Substitute $x = 1$ into $h(x)$: $h(1)=\frac{3}{1+7}=\frac{3}{8}$.

Step4: Calculate the average rate of change

$\frac{h(8)-h(1)}{8 - 1}=\frac{\frac{1}{5}-\frac{3}{8}}{7}=\frac{\frac{8-15}{40}}{7}=\frac{-\frac{7}{40}}{7}=-\frac{1}{40}$.

Answer:

$-\frac{1}{40}$