Question

given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval $18 \leq x \leq 24$.

$x$\t$f(x)$
12\t41
18\t40
24\t39
30\t38

answer

Explanation:

Step1: Recall average rate of change formula

The average rate of change of a function $f(x)$ over $[a,b]$ is $\frac{f(b)-f(a)}{b-a}$.

Step2: Identify values from the table

For $[18,24]$, $a=18$, $f(a)=40$, $b=24$, $f(b)=39$.

Step3: Substitute values into formula

$\frac{f(24)-f(18)}{24-18} = \frac{39-40}{24-18}$

Step4: Simplify the expression

$\frac{-1}{6}$

Answer:

$\frac{-1}{6}$