(a)
To find: The equation of the tangent line to the curve at the point.
(a)
Answer to Problem 24E
The equation of the tangent line to the curve
Explanation of Solution
Given:
The equation of the curve is,
Derivative rules:
(1) Constant Multiple Rule:
(2) Power Rule:
(3)
Formula used:
The equation of the tangent line at
where, m is the slope of the tangent line at
Calculation:
The derivative of
Apply the sum rule (3)
Apply the constant multiple rule(1).
Apply the power rule (2)and simplify the expressions,
Therefore, the derivative of the function
The slope of the tangent line at
Thus, the slope of the tangent line at
Substitute
Add 3 on both sides and simplify further,
Therefore, the equation of the tangent line to the curve
(b)
To sketch: The given curve and the tangent line at the given point
(b)
Explanation of Solution
Given:
The curve is
Graph:
Use the online graphing calculator to draw the graph of the functions as shown below in Figure 1.
From Figure 1, it is observed that the equation of the tangent line touches 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