Question

points) let $f(x)=\frac{3}{x - 1}$.
(4 points) find the average rate of change of $f$ on the interval $4,9$

Explanation:

Step1: Recall average rate of change formula

The average rate of change of a function $y = f(x)$ on the interval $[a,b]$ is $\frac{f(b)-f(a)}{b - a}$. Here $a = 4$, $b=9$ and $f(x)=\frac{3}{x - 1}$.

Step2: Calculate $f(4)$

Substitute $x = 4$ into $f(x)$: $f(4)=\frac{3}{4 - 1}=\frac{3}{3}=1$.

Step3: Calculate $f(9)$

Substitute $x = 9$ into $f(x)$: $f(9)=\frac{3}{9 - 1}=\frac{3}{8}$.

Step4: Calculate average rate of change

$\frac{f(9)-f(4)}{9 - 4}=\frac{\frac{3}{8}-1}{5}=\frac{\frac{3 - 8}{8}}{5}=\frac{-\frac{5}{8}}{5}=-\frac{1}{8}$.

Answer:

$-\frac{1}{8}$