To accurately describe the graph of \( f(x) \) in terms of its average rate of change, we would need to analyze the behavior of the function over the specified intervals. However, since the function \( f(x) \) itself is not provided, I can guide you through the process to determine the correct statement regarding the intervals and their average rates of change.
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Understanding Average Rate of Change: The average rate of change of a function on an interval \([a, b]\) is calculated as: \[ \text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a} \] If \( f(b) < f(a) \), then the average rate of change is negative.
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Evaluating Intervals: You would assess the value of \( f(x) \) at the endpoints of each interval stated in the responses:
- For \([0, 1]\)
- For \([1, 3]\)
- For \([3, 4]\)
- For \([6, 7]\)
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Identifying Negative Average Rates: After calculating the average rates of change for each interval, identify which intervals yield a negative average rate of change.
The statements provided can be categorized as follows:
- The average rate of change is negative only on [1, 3].
- The average rate of change is negative on [0, 1] and [3, 4].
- The average rate of change is negative only on [6, 7].
- The average rate of change is negative on both [1, 3] and [6, 7].
By following the steps and utilizing the appropriate values from the function, you can find the correct statement regarding the average rate of change for the intervals. If you have specific values or more information about \( f(x) \), feel free to share, and I can assist you further!
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