Explanation Given: The given function is y = 1 + x 2 − 2 x . Calculation: Given: the given interval is [ 0 , 1 ] . Use sum/ difference rule . ( f ± g ) ' = f ' ± g ' y = 1 + x 2 − 2 x y ' = d d x 1 + x 2 − d d x ( 2 x ) Apply chain rule. d f ( u ) d x = d f d u ⋅ d u d x y ' = d d x 1 + x 2 − d d x ( 2 x ) Let f = u , u = 1 + x 2 y ' = [ d d u u d d x ( x 2 + 1 ) ] − 2 y ' = [ 1 2 u ⋅ 2 x ] − 2 Substitute u = x 2 + 1 y ' = [ 1 x 2 + 1 ⋅ x ] − 2 y ' = x x 2 + 1 − 2 For critical point y ' = 0

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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Question

Chapter 4.2, Problem 44E

To determine

Find 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 43E

Chapter 4.2, Problem 45E

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(#1) Consider the solid bounded below by z = x² and above by z = 4-y². If we were to project this solid down onto the xy-plane, you should be able to use algebra to determine the 2D region R in the xy-plane for the purposes of integration. Which ONE of these limite of integration would correctly describe R? (a) y: x24x: -22 - (b) y: 22 x: 04-y² (c) y: -√√4-x2. →√√4x²x: −2 → 2 (d) z: 24-y² y: -2 → 2 (e) None of the above

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Chapter 4 Solutions

Loose-Leaf Version for Calculus: Early Transcendentals Single Variable

Ch. 4.1 - Prob. 1PQ Ch. 4.1 - Prob. 2PQ Ch. 4.1 - Prob. 3PQ Ch. 4.1 - Prob. 4PQ Ch. 4.1 - Prob. 1E Ch. 4.1 - Prob. 2E Ch. 4.1 - Prob. 3E Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E Ch. 4.1 - Prob. 6E

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Prob. 63CRE Ch. 4 - Prob. 64CRE Ch. 4 - Prob. 65CRE Ch. 4 - Prob. 66CRE Ch. 4 - Prob. 67CRE Ch. 4 - Prob. 68CRE Ch. 4 - Prob. 69CRE Ch. 4 - Prob. 70CRE Ch. 4 - Prob. 71CRE Ch. 4 - Prob. 72CRE Ch. 4 - Prob. 73CRE Ch. 4 - Prob. 74CRE Ch. 4 - Prob. 75CRE Ch. 4 - Prob. 76CRE Ch. 4 - Prob. 77CRE Ch. 4 - Prob. 78CRE Ch. 4 - Prob. 79CRE Ch. 4 - Prob. 80CRE Ch. 4 - Prob. 81CRE Ch. 4 - Prob. 82CRE Ch. 4 - Prob. 83CRE Ch. 4 - Prob. 84CRE Ch. 4 - Prob. 85CRE Ch. 4 - Prob. 86CRE Ch. 4 - Prob. 87CRE Ch. 4 - Prob. 88CRE Ch. 4 - Prob. 89CRE

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Find 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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Find 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