To find: All points on the graph such that the tangent line is horizontal.
Answer to Problem 49E
The required points such that the tangent line is horizontal are at
Explanation of Solution
Given:
The function is
Derivative Rule:
If
Calculation:
Obtain the derivative of
Apply the difference rule as shown in equation (1),
Simplify further and obtain the derivative,
Thus, the derivative of
Note that, the function
Here, it is sufficient to find the value of x for which
Therefore, the general solution for
Substitute
Thus, the tangent is horizontal at the point is
Substitute
Thus, the tangent is horizontal at the point is
Therefore, the required points such that the tangent line is horizontal are at
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