To determine the interval over which the function \( f(x) \) has the greatest average rate of change, we generally calculate the average rate of change over each interval as:
\[ \text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a} \]
where \( [a, b] \) is the interval in question.
Given the options and assuming you are looking for where the increase (change in \( y \)) is greatest over the specified intervals:
- [0, 1]: Calculate \( \frac{f(1) - f(0)}{1 - 0} \)
- [1, 4]: Calculate \( \frac{f(4) - f(1)}{4 - 1} \)
- [4, 5]: Calculate \( \frac{f(5) - f(4)}{5 - 4} \)
- [5, 6]: Calculate \( \frac{f(6) - f(5)}{6 - 5} \)
Without the actual graph, I can't provide specific values. However, you would need to compute these rates of change based on the values of \( f(x) \) at the endpoints of each interval. The interval with the highest computed value will indicate the greatest average rate of change.
Please calculate those for each interval using the graph or function values provided. The correct interval with the greatest average rate of change would be the one with the highest result from these calculations.
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