Explanation Given: The given function is y = x + x 2 − 2 x . Calculation: Given: the given interval is [ 0 , 4 ] . Use sum/ difference rule . ( f ± g ) ' = f ' ± g ' y = x + x 2 − 2 x y ' = d d x x + 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 x + x 2 − d d x ( 2 x ) Let f = u , u = x + x 2 and f = u , u = x y ' = [ d d u u d d x ( x + x 2 ) ] − 2 [ d d u u d d x ( x ) ] y ' = [ 1 2 u ⋅ ( 1 + 2 x ) ] − 2 [ 1 2 u ] Substitute u = x 2 + 1 and u = x y ' = [ 1 2 x 2 + x ⋅ ( 1 + 2 x ) ] − [ 1 x ] y ' = ( 1 + 2 x ) 2 x 2 + x − 1 x For critical point y ' = 0

4th Edition

ISBN: 9781319050740

Author: Jon Rogawski, Colin Adams, Robert Franzosa

Publisher: W. H. Freeman

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Question

Chapter 4.2, Problem 45E

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 44E

Chapter 4.2, Problem 46E

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Chapter 4 Solutions

Calculus: Early Transcendentals

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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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