the function y = f(x) is graphed below. what is the average rate of change of the function f(x) on the…
the function y = f(x) is graphed below. what is the average rate of change of the function f(x) on the interval 2 ≤ x ≤ 7?
Answer
Explanation:
Step1: Recall average - rate - of - change formula
The average rate of change of a function $y = f(x)$ on the interval $[a,b]$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a = 2$ and $b=7$.
Step2: Find $f(2)$ and $f(7)$ from the graph
From the graph, when $x = 2$, $f(2)=- 5$; when $x = 7$, $f(7)=40$.
Step3: Calculate the average rate of change
Substitute $a = 2$, $b = 7$, $f(2)=-5$ and $f(7)=40$ into the formula: $\frac{f(7)-f(2)}{7 - 2}=\frac{40-(-5)}{7 - 2}=\frac{40 + 5}{5}=\frac{45}{5}=9$.
Answer:
9