Concept explainers
Explain that the given curve has two tangent lines at the origin.
Explanation of Solution
Given:
The given equations are
Calculation:
Find the slope.
Apply formula
Apply chain rule.
Let
Apply sum/difference rule.
Use derivative rule
Substitute the value of
Use derivative rules
Find the value of the parameter
At
At
There are two different tangents at the origin because there is two different slope values.
Now use point-slope form for the tangent equations.
The graph of the given curve and the tangent lines is given below.
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