Question

given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval $2 \leq x \leq 6$.
$x$\t$f(x)$
0\t20
2\t30
4\t40
6\t50
8\t60
10\t70
answer attempt 1 out of 2

Explanation:

Step1: Recall average rate 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 table

For interval $2 \leq x \leq 6$, $a=2$, $f(a)=30$, $b=6$, $f(b)=50$.

Step3: Substitute into formula

$\frac{f(6)-f(2)}{6-2} = \frac{50-30}{6-2}$

Step4: Calculate the result

$\frac{20}{4} = 5$

Answer:

5