To find: The points at which the slope of the curve is -1.
Answer to Problem 51E
The slope of the curve is -1 at the points
Explanation of Solution
Given:
The curve
Derivative rules:
Product rule:
Chain rule:
Calculation:
Differentiate
Apply the product rule,
Apply the chain rule and simplify the terms,
Thus, the derivative of the equation is
That is, the slope of the tangent is
Obtain the required points such that the slope of the tangent is -1.
Simplify the expression,
Substitute
That is,
Therefore, the equation
Substitute
Let
Thus, the real solution are
Substitute
Therefore, the slope of the curve is -1 at the point
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