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 1 ≤ x ≤ 2?
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, $a = 1$ and $b = 2$.
Step2: Find $f(1)$ and $f(2)$ from the graph
From the graph, when $x = 1$, $f(1)=10$. When $x = 2$, $f(2)=0$.
Step3: Calculate the average rate of change
Substitute $a = 1$, $b = 2$, $f(1)=10$, and $f(2)=0$ into the formula: $\frac{f(2)-f(1)}{2 - 1}=\frac{0 - 10}{1}=- 10$.
Answer:
$-10$