Concept explainers
To find: The equation of the tangent line to the given curve at the given point.
Answer to Problem 21E
The equation of the tangent line to the curve
Explanation of Solution
Given:
The curve is
The point is
Derivative rules:
Chain rule
If
Formula used:
The equation of the tangent line at
where, m is the slope of the tangent line at
Calculation:
Consider
Differentiate the above equation implicitly with respect to x,
Apply the chain rule (1) and simplify the terms,
Combine the terms of
Therefore, the derivative of y is
The slope of the tangent line at
Substitute the values
Thus, the slope of the tangent line at
Substitute
Therefore, the equation of the tangent line to the curve
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