Math Problem Statement
find the average rate of change if N(p) = 90- 3psquared find the average rate of change from 3 to 4 dollars and N(p) is boxes of nails at p dollars per box
Solution
The average rate of change of a function over an interval is given by the formula:
Given function:
Interval: to
Step 1: Compute
Step 2: Compute
Step 3: Compute the average rate of change
Final Answer:
This means that as the price increases from $3 to $4, the number of boxes of nails sold decreases by 21 on average per dollar increase.
Do you need a more detailed explanation or have any questions?
Here are some related questions:
- What does a negative average rate of change indicate?
- How would the rate of change differ if we used a different interval?
- What is the instantaneous rate of change at ?
- How does the function behave for large values of ?
- What happens if the price keeps increasing—will ever be negative?
Tip: The average rate of change is the slope of the secant line connecting two points on a function's graph.
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Math Problem Analysis
Mathematical Concepts
Algebra
Rate of Change
Quadratic Functions
Formulas
Average Rate of Change = (N(b) - N(a)) / (b - a)
Theorems
Slope of the Secant Line
Suitable Grade Level
Grades 9-12
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