Calculus: Graphical, Numerical, Algebraic, 3rd Edition Answers Ch 3 Derivatives Ex 3.2
Calculus: Graphical, Numerical, Algebraic Answers
Chapter 3 Derivatives Exercise 3.2 1E
Chapter 3 Derivatives Exercise 3.2 1QR
Chapter 3 Derivatives Exercise 3.2 2E
Chapter 3 Derivatives Exercise 3.2 2QR
Chapter 3 Derivatives Exercise 3.2 3E
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Chapter 3 Derivatives Exercise 3.2 4E
For Left-hand derivative, function is y = x
So, left-hand derivative is given by:
Chapter 3 Derivatives Exercise 3.2 4QR
Chapter 3 Derivatives Exercise 3.2 5E
(a) Differentiable: At all the points in the interval [-3, 2].
Since, there are no any corners, cusps, vertical tangent lines, or point of discontinuity within this domain. The graph of the function is unbroken and smooth, with well defined slopes at each point.
(b) Continuous but not differentiable: None
Since the function is differentiable at all the points in the domain.
(c) Neither continuous nor differentiable: None
Since the function is differentiable at all the points in the domain; it also implies that the function is continuous at all the points in the domain interval.
Chapter 3 Derivatives Exercise 3.2 5QR
Chapter 3 Derivatives Exercise 3.2 6E
(a) Differentiable: At all the points in the interval [-2,3].
Since, there are no any corners, cusps, vertical tangent lines, or point of discontinuity within this domain. The graph of the function is unbroken and smooth, with well defined slopes at each point.
(b) Continuous but not differentiable: None
Since the function is differentiable at all the points in the domain.
(c) Neither continuous nor differentiable: None
Since the function is differentiable at all the points in the domain; it also implies that the function is continuous at all the points in the domain interval.
Chapter 3 Derivatives Exercise 3.2 6QR
Chapter 3 Derivatives Exercise 3.2 7E
Chapter 3 Derivatives Exercise 3.2 7QR
Chapter 3 Derivatives Exercise 3.2 8E
Chapter 3 Derivatives Exercise 3.2 8QR
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Chapter 3 Derivatives Exercise 3.2 9QR
Chapter 3 Derivatives Exercise 3.2 10E
Chapter 3 Derivatives Exercise 3.2 10QR
Chapter 3 Derivatives Exercise 3.2 11E
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Chapter 3 Derivatives Exercise 3.2 14E
Chapter 3 Derivatives Exercise 3.2 15E
Here, one-sided derivative differs from the other.
Therefore this is a problem of corner.
Hence, the problem is a corner.
Chapter 3 Derivatives Exercise 3.2 16E
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