Question
Average Rate of Change Quick Check
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Question
Use the image to answer the question.
A coordinate plane for f of x versus x.
Given the graph of f(x) , on which interval is the average rate of change the greatest?
(1 point)
Responses
The function has the greatest average rate of change over the interval [1,4].
The function has the greatest average rate of change over the interval left bracket 1 comma 4 right bracket .
The function has the greatest average rate of change over the interval [4,5].
The function has the greatest average rate of change over the interval left bracket 4 comma 5 right bracket .
The function has the greatest average rate of change over the interval [0,1].
The function has the greatest average rate of change over the interval left bracket 0 comma 1 right bracket .
The function has the greatest average rate of change over the interval [5,6].
The function has the greatest average rate of change over the interval left bracket 5 comma 6 right bracket .
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Answers
Answered by
GPT-4o mini
To determine on which interval the average rate of change of the function is greatest, you would typically calculate the average rate of change on each given interval and compare the values.
Recall that the formula for the average rate of change of a function \( f(x) \) over an interval \([a, b]\) is:
\[
\text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a}
\]
Since you mentioned a graph but did not provide specific details or data points, I can guide you on how you could approach the problem:
1. **Identify the Intervals**: For each given interval ([0,1], [1,4], [4,5], and [5,6]), identify the values of \( f(x) \) at the endpoints \( a \) and \( b \).
2. **Calculate the Rates**: For each interval, use the formula to compute the average rate of change.
3. **Compare the Results**: Determine which calculation yields the highest average rate of change.
If you have access to the graph and can identify the values of \( f(x) \) at the specified points, follow these steps for each interval:
- **For [0,1]**: Calculate \( \frac{f(1) - f(0)}{1 - 0} \)
- **For [1,4]**: Calculate \( \frac{f(4) - f(1)}{4 - 1} \)
- **For [4,5]**: Calculate \( \frac{f(5) - f(4)}{5 - 4} \)
- **For [5,6]**: Calculate \( \frac{f(6) - f(5)}{6 - 5} \)
Choose the interval with the highest computed average rate of change. If you have specific values from the graph, feel free to share them, and I can assist you further!
Recall that the formula for the average rate of change of a function \( f(x) \) over an interval \([a, b]\) is:
\[
\text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a}
\]
Since you mentioned a graph but did not provide specific details or data points, I can guide you on how you could approach the problem:
1. **Identify the Intervals**: For each given interval ([0,1], [1,4], [4,5], and [5,6]), identify the values of \( f(x) \) at the endpoints \( a \) and \( b \).
2. **Calculate the Rates**: For each interval, use the formula to compute the average rate of change.
3. **Compare the Results**: Determine which calculation yields the highest average rate of change.
If you have access to the graph and can identify the values of \( f(x) \) at the specified points, follow these steps for each interval:
- **For [0,1]**: Calculate \( \frac{f(1) - f(0)}{1 - 0} \)
- **For [1,4]**: Calculate \( \frac{f(4) - f(1)}{4 - 1} \)
- **For [4,5]**: Calculate \( \frac{f(5) - f(4)}{5 - 4} \)
- **For [5,6]**: Calculate \( \frac{f(6) - f(5)}{6 - 5} \)
Choose the interval with the highest computed average rate of change. If you have specific values from the graph, feel free to share them, and I can assist you further!
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