Concept explainers
(a)
To describe: The meaning for f to be differentiable at a.
(a)
Explanation of Solution
If a is appoint in the domain of a function f, then f is said to be differentiable at a if the derivative
(b)
To describe: The relation between differentiability and continuity.
(b)
Explanation of Solution
All differentiable functions are continuous, but not all the continuous functions are differentiable.
Let a function
Function
Since, x approaches
Take limit as x approaches to
Hence
Since there exist
(c)
To sketch: A function that is continuous but not differentiable at
(c)
Explanation of Solution
Example:
Let the function
Graph:
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