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 $6leq xleq7$?
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, $a = 6$ and $b = 7$.
Step2: Read function values from the graph
From the graph, when $x = 6$, $f(6)=0$. When $x = 7$, assume the value of $y$ (i.e., $f(7)$) is 4.
Step3: Calculate the average rate of change
Substitute $a = 6$, $b = 7$, $f(6)=0$, and $f(7)=4$ into the formula $\frac{f(b)-f(a)}{b - a}$. We get $\frac{f(7)-f(6)}{7 - 6}=\frac{4 - 0}{1}=4$.
Answer:
4