Concept explainers
(a)
To find: The rate of change of F with respect to
(a)
Answer to Problem 38E
The rate of change of F with respect to
Explanation of Solution
Given:
The magnitute of the force is
Where,
Derivative Rule:
If
Calculation:
Obtain the derivative of F.
Apply Quotient Rule as shown equation (1),
Therefore, the rate of change of F with respect to
(b)
To find: The value of
(b)
Answer to Problem 38E
The rate of change equal to zero when
Explanation of Solution
Given:
From part (a), the rate of change of F with respect to
Calculation:
The rate of change equal to zero,
Since
Therefore, the rate of change equal to zero when
(c)
To draw:. The graph of F as a function of
(c)
Explanation of Solution
Given:
The magnitute of the force is
Use online graphing calculator to draw the graph of F as a function of
The value of
Calculation:
Obtain the magnitute of the force F as a function of
Substitute
Therefore, the magnitute of the force F as a function of
From part (b), the rate of change equal to zero when
Substitute
Therefore, the value of
Substitute
Therefore, the point
Use online graphing calculator and draw the graph of F as a function of
From Figure 1, it is observed that the slope of tangent is horizontanl to the curve
Hence, the value 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