given the function defined in the table below, find the average rate of change of the function over the…
given the function defined in the table below, find the average rate of change 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 given by $\frac{f(b)-f(a)}{b - a}$. Here, $a = 3$, $b = 6$.
Step2: Identify $f(a)$ and $f(b)$ from the table
When $a = 3$, $f(3)=10$; when $b = 6$, $f(6)=80$.
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:
$\frac{70}{3}$