To determine the interval with the greatest average rate of change for the function \( f(x) \), we calculate the average rate of change for each of the given intervals. The average rate of change over an interval \([a, b]\) is given by the formula:
\[ \text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a} \]
You would need to analyze the function’s values at the endpoints of each interval specified:
- Interval [0,1]: Calculate \( \frac{f(1) - f(0)}{1 - 0} \)
- Interval [1,4]: Calculate \( \frac{f(4) - f(1)}{4 - 1} \)
- Interval [4,5]: Calculate \( \frac{f(5) - f(4)}{5 - 4} \)
- Interval [5,6]: Calculate \( \frac{f(6) - f(5)}{6 - 5} \)
By comparing the computed values for these intervals, the interval that yields the largest value will indicate where the function has the greatest average rate of change.
Since I cannot see the image you refer to, I recommend this approach for your analysis. If you can provide numeric values or specific characteristics from the graph, I can help you determine which interval has the greatest average rate of change based on that information.
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