Concept explainers
The cost function for a certain commodity is
C(q) = 84 + 0.16q – 0.0006q2 + 0.000003q3
(a) Find and interpret C′(100).
(b) Compare C′(100) with the cost of producing the 101st item.
(a)
To find: The value of
Answer to Problem 30E
The value of
Explanation of Solution
The cost function is
Obtain the derivative of the cost function.
Substitute q = 100 in
The value of
(b)
To find: Compare the values of
Answer to Problem 30E
The cost of manufacturing the 101st pair of jeans is approximately $0.13.
Explanation of Solution
The cost function is
From part (a),
The cost of manufacturing the 101st item is calculated by,
Substitute x = 100 in
Substitute x = 101 in
Substitute the respective values in
The cost of manufacturing the 101st pair of jeans is approximately $0.13, which is very close to the cost of
Chapter 3 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced Edition
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning