10. values of a function are given in the table below. what is the average rate of change of the function on…
10. values of a function are given in the table below. what is the average rate of change of the function on the interval 1,11?\n| x | f(x) |\n| -2 | 4 |\n| 1 | 7 |\n| 5 | 11 |\n| 8 | 8 |\n| 11 | 6 |\n| 14 | 2 |\na -1/10\nb 1/10\nc -8/3\nd 8/3
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, $a = 1$, $b = 11$.
Step2: Find $f(a)$ and $f(b)$ from the table
When $x=a = 1$, $f(1)=7$; when $x = b=11$, $f(11)=6$.
Step3: Calculate the average rate of change
Substitute into the formula: $\frac{f(11)-f(1)}{11 - 1}=\frac{6 - 7}{10}=\frac{-1}{10}$.
Answer:
A. $\frac{-1}{10}$