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Calculus: Graphical, Numerical, Algebraic, 3rd Edition Answers Ch 3 Derivatives Ex 3.4

Calculus: Graphical, Numerical, Algebraic Answers

Chapter 3 Derivatives Exercise 3.4 1E

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Chapter 3 Derivatives Exercise 3.4 2E

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Chapter 3 Derivatives Exercise 3.4 11E

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(d) The horse is running the fastest during the last furlong (between 9th and 10th furlong markers). This furlong takes only 11 seconds to run, which is the least amount of time for a furlong.
(e) The horse accelerates the fastest during the first furlong (between markers 0 and 1) because horse starts with zero speed and reaches to a great speed so the rate of change of speed is largest during the first furlong.

Chapter 3 Derivatives Exercise 3.4 13E

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In the given figure graph C is position, graph A is velocity and graph B is acceleration. Because A is the derivative of C as we see that it is positive, negative and zero where C is increasing, decreasing and has horizontal tangents, respectively. The relationship between B and A is similar.

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Calculus: Graphical, Numerical, Algebraic, 3rd Edition Answers Ch 3 Derivatives Ex 3.3

Calculus: Graphical, Numerical, Algebraic Answers

Chapter 3 Derivatives Exercise 3.3 1E

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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

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Chapter 3 Derivatives Exercise 3.2 2E

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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:

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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.

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Here, one-sided derivative differs from the other.
Therefore this is a problem of corner.
Hence, the problem is a corner.

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Calculus: Graphical, Numerical, Algebraic, 3rd Edition Answers Ch 3 Derivatives Ex 3.1

Calculus: Graphical, Numerical, Algebraic Answers

Chapter 3 Derivatives Exercise 3.1 1E

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(e) We will look for the steepest part of the curve. This is where the elevation is dropping most rapidly and therefore the most likely location for significant “rapids.”
These are points where there is significant change in river elevation, causes rapid increase in the speed of the river flow and hence becomes the most dangerous section of the river.
(f) We will look for the lowest point on the graph. This is where the elevation is dropping most rapidly and therefore the most likely location for significant “rapids.”
These are points where there is significant change in depth, and hence becomes the most dangerous section of the river.

Chapter 3 Derivatives Exercise 3.1 31E

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