Question
Use the average rate of change to describe the graph of f(x) over the interval [0, 2].
(1 point)
The average rate of change is −2.
The average rate of change is zero.
The average rate of change is −
1
2
.
The average rate of change is 2
(1 point)
The average rate of change is −2.
The average rate of change is zero.
The average rate of change is −
1
2
.
The average rate of change is 2
Answers
GPT-4o mini
To determine the average rate of change of a function \( f(x) \) over the interval \([a, b]\), you can use the formula:
\[
\text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a}
\]
For the interval \([0, 2]\), we would compute:
\[
\text{Average Rate of Change} = \frac{f(2) - f(0)}{2 - 0} = \frac{f(2) - f(0)}{2}
\]
However, in order to provide a specific answer from the options listed (−2, 0, −1/2, or 2), we would need the specific values of \( f(0) \) and \( f(2) \).
- If \( f(2) < f(0) \), the average rate of change could be negative.
- If \( f(2) = f(0) \), the average rate of change would be zero.
- If \( f(2) > f(0) \), the average rate of change would be positive.
If you have the specific values of \( f(0) \) and \( f(2) \), please provide them so I can help calculate the average rate of change and confirm which option is correct!
\[
\text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a}
\]
For the interval \([0, 2]\), we would compute:
\[
\text{Average Rate of Change} = \frac{f(2) - f(0)}{2 - 0} = \frac{f(2) - f(0)}{2}
\]
However, in order to provide a specific answer from the options listed (−2, 0, −1/2, or 2), we would need the specific values of \( f(0) \) and \( f(2) \).
- If \( f(2) < f(0) \), the average rate of change could be negative.
- If \( f(2) = f(0) \), the average rate of change would be zero.
- If \( f(2) > f(0) \), the average rate of change would be positive.
If you have the specific values of \( f(0) \) and \( f(2) \), please provide them so I can help calculate the average rate of change and confirm which option is correct!