question given the function defined in the table below, find the average rate of change, in simplest form…

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 ≤ x ≤ 6. x f(x) 2 5 3 10 4 20 5 40 6 80 7 160

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 ≤ x ≤ 6. x f(x) 2 5 3 10 4 20 5 40 6 80 7 160

Answer

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, $a = 3$ and $b = 6$.

Step2: Find $f(3)$ and $f(6)$ from the table

From the table, when $x = 3$, $f(3)=10$; when $x = 6$, $f(6)=80$.

Step3: Calculate the average rate of change

Substitute into the formula: $\frac{f(6)-f(3)}{6 - 3}=\frac{80 - 10}{3}=\frac{70}{3}$.

Answer:

$\frac{70}{3}$