nction defined in the table below, find the average rate on over the interval 5 ≤ x ≤ 7. x f(x) 1 26 3 12 5…
nction defined in the table below, find the average rate on over the interval 5 ≤ x ≤ 7. x f(x) 1 26 3 12 5 6 7 8
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, $a = 5$, $b = 7$.
Step2: Identify $f(a)$ and $f(b)$ from the table
When $a = 5$, $f(5)=6$; when $b = 7$, $f(7)=8$.
Step3: Calculate the average rate of change
Substitute into the formula: $\frac{f(7)-f(5)}{7 - 5}=\frac{8 - 6}{2}=\frac{2}{2}=1$.
Answer:
$1$