Question

given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 40 ≤ x ≤ 55.

x	f(x)
25	23
40	17
55	11
70	5
85	-1

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, $a = 40$, $b = 55$, $f(a)=f(40)=17$, and $f(b)=f(55)=11$.

Step2: Substitute values into formula

Substitute $a = 40$, $b = 55$, $f(40)=17$, and $f(55)=11$ into the formula $\frac{f(b)-f(a)}{b - a}$. We get $\frac{11 - 17}{55-40}$.

Step3: Simplify the expression

First, calculate the numerator: $11-17=-6$. Then, calculate the denominator: $55 - 40 = 15$. So, $\frac{-6}{15}=-\frac{2}{5}$.

Answer:

$-\frac{2}{5}$