Question

question: given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 4 ≤ x ≤ 6.

x	3	4	5	6
f(x)	8	12	18	26

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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, $a = 4$, $b=6$, $f(4)=12$ and $f(6)=26$.

Step2: Substitute values into formula

$\frac{f(6)-f(4)}{6 - 4}=\frac{26 - 12}{2}$.

Step3: Simplify the expression

$\frac{14}{2}=7$.

Answer:

$7$