To calculate: The equation of tangent line to the curve
Answer to Problem 34E
The equation of tangent line to the curve
Explanation of Solution
Given information:
The equation of curve
Formula used:
Thechain rule for differentiation is if f is a function of gthen
Power rule for differentiation is
Product rule for differentiation is
Derivative of
The point slope form of an equation is
Calculation:
Consider the equation of curve
Differentiate both sides with respect to x ,
Recall that power rule for differentiation is
Apply it.
Recall that the point slope form of an equation is
It is provided that the curve passes through the point
Substitute x as 1, in the derivative found above,
Therefore, slope is
Now, the equation of tangent line to the curve
Thus, the equation of 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