Math Problem Statement
Solution
The question asks: On which interval does the function decrease the most?
The table shows the average rate of change for different intervals:
- :
- :
- :
- :
The function decreases the most where the average rate of change is the most negative. The interval with the most negative rate of change is , where the rate is . This matches the answer you selected.
Let me know if you need further clarifications!
Here are 5 follow-up questions:
- What does the average rate of change of a function tell you about its behavior on a specific interval?
- How would the rate of change differ for a function that is increasing vs decreasing?
- How can you compute the average rate of change for any given interval if not provided?
- What does it mean if the rate of change is zero over an interval?
- How would you interpret a positive average rate of change in comparison to a negative one?
Tip: The average rate of change of a function over an interval is essentially the slope of the line connecting the endpoints of the interval on the function graph.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Calculus
Average Rate of Change
Formulas
Average Rate of Change = (Change in Function Value) / (Change in Variable)
Theorems
Rate of Change Interpretation
Suitable Grade Level
High School - Grades 10-12