ne function defined in the table below, find the average rate of nction over the interval 4 ≤ x ≤ 6. x f(x)…
ne function defined in the table below, find the average rate of nction over the interval 4 ≤ x ≤ 6. x f(x) 2 10 3 8 4 8 5 10 6 14
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, $a = 4$, $b = 6$.
Step2: Identify $f(a)$ and $f(b)$
From the table, when $a = 4$, $f(4)=8$; when $b = 6$, $f(6)=14$.
Step3: Calculate the average rate of change
Substitute into the formula: $\frac{f(6)-f(4)}{6 - 4}=\frac{14 - 8}{2}$. $\frac{14 - 8}{2}=\frac{6}{2}=3$.
Answer:
$3$