Question

given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval $3 \leq x \leq 6$.
$x$\t$f(x)$
2\t5
3\t10
4\t20
5\t40
6\t80
7\t160
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 $a=3$, $f(3)=10$; for $b=6$, $f(6)=80$.

Step3: Substitute into formula

$$\frac{f(6)-f(3)}{6-3} = \frac{80-10}{6-3}$$

Step4: Simplify the expression

$$\frac{70}{3}$$

Answer:

$\frac{70}{3}$