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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Chapter 4 Solutions

Loose-Leaf Version for Calculus: Early Transcendentals Single Variable

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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