Explanation Given: The given function is y = cos θ + sin θ . Calculation: Given: the given interval is [ 0 , 2 π ] . Use sum/ difference rule . ( f + g ) ' = f ' + g ' Now differentiate the function using above rule of derivative. y = cos θ + sin θ y ' = d d θ ( cos θ ) + d d θ ( sin θ ) y ' = − sin θ + cos θ For critical point y ' = 0 . − sin θ + cos θ = 0 ⇒ − sin θ + cos θ + sin θ = sin θ ⇒ cos θ = sin θ ⇒ cos θ cos θ = sin θ cos θ ⇒ 1 = tan θ ⇒ tan θ = 1 θ = π 4 + 2 n π , 5 π 4 + 2 n π Now,

Loose-Leaf Version for Calculus: Early Transcendentals Single Variable

4th Edition

ISBN: 9781319312886

Author: Rogawski, Jon, Adams, Colin, FRANZOSA, Robert

Publisher: W. H. Freeman

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

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Question

Chapter 4.2, Problem 52E

To determine

The minimum and maximum values of the given function in the given interval by comparing with critical and end points.

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Chapter 4.2, Problem 51E

Chapter 4.2, Problem 53E

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Chapter 4 Solutions

Loose-Leaf Version for Calculus: Early Transcendentals Single Variable

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The minimum and maximum values of the given function in the given interval by comparing with critical and end points.

Solution Summary: The author calculates the minimum and maximum values of a given function in the given interval by comparing with critical and end points.

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The minimum and maximum values of the given function in the given interval by comparing with critical and end points.

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Chapter 4 Solutions