Concept explainers
(a)
To Show: The function
(a)
Explanation of Solution
Result Used: The derivative of a function at
Proof:
Consider the function,
Compute
Here, the function
Therefore, the derivative of the function does not exist at
Thus, the required proof is obtained.
(b)
To find: The value of
(b)
Answer to Problem 50E
The value of derivative of
Explanation of Solution
Given:
The function
Calculation:
Obtain the derivative of the function
Compute
Simplify further,
Thus the value of the derivative at
(c)
To Show: The
(c)
Explanation of Solution
Result Used:
A curve has a vertical tangent line at
Proof:
Consider the equation
Substitute
Thus
The limit of the function
Therefore,
From part (b),
Take the limit of the function
Since the function
By result, the curve
Thus, the curve
(d)
To illustrate: Thepart (c) by graphing
(d)
Explanation of Solution
Graph:
Use the online graphing calculator to draw the graph of the function
Illustration:
From Figure 1, it is clear that the y-axis is the vertical tangent to the curve
Chapter 2 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