Question

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

Step3: Substitute into formula

$\frac{f(4)-f(3)}{4-3} = \frac{4-4}{4-3}$

Step4: Simplify the expression

$\frac{0}{1} = 0$

Answer:

0