Concept explainers
Instantaneous Rate of Change The following data represent the total revenue (in dollars) received from selling bicycles at Tunney’s Bicycle Shop.
(a) Find the average rate of change in revenue from to bicycles.
(b) Find the average rate of change in revenue from to bicycles. per bicycle
(c) Find the average rate of change in revenue from to bicycles. per bicycle
(d) Using a graphing utility, find the quadratic function of best fit.
(e) Using the function found in part (d), determine the instantaneous rate of change of revenue at bicycles.
To find: Instantaneous Rate of Change The following data represent the total revenue (in dollars) received from selling bicycles at Tunney's Bicycle Shop.
a. Find the average rate of change in revenue from bicycles.
Answer to Problem 50AYU
Solution:
a.
Explanation of Solution
Given:
Calculation:
a. The average rate of change in revenue from is,
To find: Instantaneous Rate of Change The following data represent the total revenue (in dollars) received from selling bicycles at Tunney's Bicycle Shop.
b. Find the average rate of change in revenue from bicycles. per bicycle.
Answer to Problem 50AYU
Solution:
b.
Explanation of Solution
Given:
Calculation:
b. The average rate of change in revenue from is,
To find: Instantaneous Rate of Change The following data represent the total revenue (in dollars) received from selling bicycles at Tunney's Bicycle Shop.
c. Find the average rate of change in revenue from bicycles. per bicycle.
Answer to Problem 50AYU
Solution:
c.
Explanation of Solution
Given:
Calculation:
c. The average rate of change in revenue from is,
To find: Instantaneous Rate of Change The following data represent the total revenue (in dollars) received from selling bicycles at Tunney's Bicycle Shop.
d. Using a graphing utility, find the quadratic function of best fit.
Answer to Problem 50AYU
Solution:
d.
Explanation of Solution
Given:
Calculation:
d. Using a graphing utility, find the quadratic function of best fit.
The quadratic function is .
To find: Instantaneous Rate of Change The following data represent the total revenue (in dollars) received from selling bicycles at Tunney's Bicycle Shop.
e. Using the function found in part , determine the instantaneous rate of change of revenue at bicycles.
Answer to Problem 50AYU
Solution:
e.
Explanation of Solution
Given:
Calculation:
e. The instantaneous rate of change of is the derivative : that is,
Replace by . the instantaneous rate of change is,
The instantaneous rate of change at is,
Chapter 14 Solutions
Precalculus Enhanced with Graphing Utilities
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