Concept explainers
To find: The points on the lemniscate where the tangent is horizontal.
Answer to Problem 39E
The points on the lemniscate where the tangent is horizontal are
Explanation of Solution
Given:
The equation is
Derivative rule: Chain rule
If
Calculation:
Obtain the point at which the tangent line is horizontal.
Consider the equation
Differentiate implicitly with respect to x,
Let
Apply the chain rule (1) and simplify the terms,
Substitute
Combine the terms
Thus, the derivative of the equation is
Note that, the tangent is horizontal if
Substitute
Simplify the terms and obtain the value of y,
Substitute
Therefore, the tangent line is horizontal at the points
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