a.
To calculate: The points where the function is differentiable.
a.
Answer to Problem 5E
The function is differentiable at every point in 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.
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 5E
There are no points in the domain 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 no break points so it the function is continuous.
From the graph it is clear that the graph is smooth without any sharp turns.
Conclusion: No, there are no such points in the domain
c.
To calculate: The function is neither continuous nor differentiable.
c.
Answer to Problem 5E
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 are no points where the function is neither continuous nor differentiable.
Conclusion: There are no such points where the function is neither continuous nor differentiable.
Chapter 2 Solutions
Advanced Placement Calculus Graphical Numerical Algebraic Sixth Edition High School Binding Copyright 2020
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