To determine the interval where the average rate of change of the function \( f(x) \) is greatest, we need to calculate the average rate of change over each provided interval. The average rate of change of a function \( f(x) \) over an interval \([a, b]\) is given by:
\[ \text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a} \]
Steps to calculate the average rate of change:
- Identify the function's values at the endpoints of each interval.
- Compute the average rate of change for each interval.
- Compare the calculated average rates of change to find the greatest one.
Here is how you can analyze each of the provided intervals if you have the graph:
- 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 \( \frac{f(6) - f(5)}{6 - 5} \)
After calculating these values by looking at the graph:
- Determine which one has the largest value.
- The interval with the highest average rate of change is the answer.
Based on your responses, you would need to check these calculations against the graph to decide which one is indeed the greatest. If you provide the values at the endpoints for each interval from the graph, I can assist you further!
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