a.
To calculate: The points where the function is differentiable.
a.
Answer to Problem 7E
The function is differentiable at every point of the domain
Explanation of Solution
Given information:
The domain is
Concept used:
If a function is differentiable at a point it will also be continuous at that point.
If a function is continuous at a point then it may or may not be differentiable.
Calculation:
From the graph it is clear that the graph is smooth without any sharp turns.
There is one exception that is at point
Conclusion: The function is differentiable at every point of the domain
b.
To calculate: The function is continuous but not differentiable.
b.
Answer to Problem 7E
There is no point where the function is continuous but not differentiable.
Explanation of Solution
Given information:
The domain is
Concept used:
If a function is continuous but not differentiable it can have corner, cusp or vertical tangent.
Calculation:
The graph has a break point at
From the graph it is clear that the graph is not smooth at
Conclusion: There is no point where the function is continuous but not differentiable.
c.
To calculate: The function is neither continuous nor differentiable.
c.
Answer to Problem 7E
No, there are no such points where the function is neither continuous nor differentiable.
Explanation of Solution
Given information:
The domain is
Concept used:
If a function is differentiable at a point it will also be continuous at that point.
If a function is continuous at a point then it may or may not be differentiable.
Calculation:
There is a point
Conclusion: There are no such points where the function is neither continuous nor differentiable.
Chapter 2 Solutions
CALCULUS:GRAPHICAL,...,AP ED.-W/ACCESS
- 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