To find the average rate of change of the function over the interval [tex]\(3 \leq x \leq 4\)[/tex] using the given table, follow these steps:
1. Identify the relevant data points: We need the values of the function at [tex]\(x = 3\)[/tex] and [tex]\(x = 4\)[/tex].
- According to the table:
- At [tex]\(x = 3\)[/tex], [tex]\(f(3) = 4\)[/tex]
- At [tex]\(x = 4\)[/tex], [tex]\(f(4) = 4\)[/tex]
2. Use the average rate of change formula: The formula for the average rate of change of a function [tex]\( f(x) \)[/tex] over an interval [tex]\( [a, b] \)[/tex] is:
[tex]\[
\text{Average rate of change} = \frac{f(b) - f(a)}{b - a}
\][/tex]
In this case, [tex]\(a = 3\)[/tex] and [tex]\(b = 4\)[/tex].
3. Substitute the values into the formula and compute:
[tex]\[
\text{Average rate of change} = \frac{f(4) - f(3)}{4 - 3}
\][/tex]
Substituting the function values, we get:
[tex]\[
\text{Average rate of change} = \frac{4 - 4}{4 - 3} = \frac{0}{1} = 0
\][/tex]
So, the average rate of change of the function over the interval [tex]\(3 \leq x \leq 4\)[/tex] is [tex]\(0\)[/tex].
