Math Problem Statement
Solution
To find the average rate of change of the function on the interval , we can use the formula for the average rate of change:
where and in this case.
Step-by-Step Solution
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Identify : From the graph, we observe that when , .
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Identify : Similarly, when , .
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Apply the formula:
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Substitute values:
Answer
The average rate of change of on the interval is .
Would you like further details on this solution, or do you have any other questions?
Here are some additional related questions to explore:
- What is the interpretation of the average rate of change in terms of slope?
- How would the average rate of change differ if we chose a different interval?
- Can we find the instantaneous rate of change at a specific point within this interval?
- What would be the effect on the average rate of change if had different values at and ?
- How does the average rate of change relate to the behavior of the graph on the chosen interval?
Tip: The average rate of change over an interval gives the slope of the secant line between the two endpoints on the graph.
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Math Problem Analysis
Mathematical Concepts
Average Rate of Change
Graph Analysis
Functions
Formulas
Average Rate of Change formula: (f(b) - f(a)) / (b - a)
Theorems
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Suitable Grade Level
Grades 9-12
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