question given the table of values below, find the average rate of change of the function f(x) on the…
question given the table of values below, find the average rate of change of the function f(x) on the interval 4,11. enter your answer as a reduced improper fraction, if necessary. provide your answer below. x f(x) 3 36 4 49 5 58 6 75 7 76 8 88 9 100 10 122 11 126 12 129
Answer
Explanation:
Step1: Recall average rate of change formula
The average rate of change of a function $f(x)$ on the interval $[a,b]$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a = 4$ and $b=11$.
Step2: Identify $f(a)$ and $f(b)$ from the table
When $x = 4$, $f(4)=49$. When $x = 11$, $f(11)=126$.
Step3: Calculate the average rate of change
Substitute into the formula: $\frac{f(11)-f(4)}{11 - 4}=\frac{126 - 49}{7}=\frac{77}{7}=11$.
Answer:
$11$