Math Problem Statement
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Solution
The table in the image shows the average rate of change for a function over four intervals. The values of the rate of change indicate how much the function is increasing or decreasing in each interval. A negative rate of change means the function is decreasing in that interval.
Here are the average rates of change for each interval:
- For , the rate of change is .
- For , the rate of change is .
- For , the rate of change is .
- For , the rate of change is .
Question:
"On which of the intervals does the function decrease the most?"
Solution:
To determine where the function decreases the most, we need to find the interval with the most negative rate of change (the largest negative number).
- is the most negative value, which corresponds to the interval .
Thus, the function decreases the most in the interval .
Would you like more details on how to interpret the average rate of change? Here are five related questions to expand your understanding:
- What does the rate of change represent in terms of a function's graph?
- How do you calculate the average rate of change between two points?
- What does it mean if the average rate of change is positive?
- How can you determine if a function is increasing or decreasing over an interval?
- How would the answer change if one of the intervals had a positive rate of change?
Tip: A more negative rate of change indicates a steeper decrease in the function's value over the given interval.
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Math Problem Analysis
Mathematical Concepts
Average Rate of Change
Functions
Intervals
Formulas
Average Rate of Change = (f(b) - f(a)) / (b - a)
Theorems
Rate of Change Theorem
Suitable Grade Level
Grades 9-11