Explanation Given: The given function is y = 3 e x − e 2 x . Calculation: The given interval is [ − 1 2 , 1 ] . Use sum/ difference rule : ( f − g ) ' = f ′ − g ′ y = 3 e x − e 2 x y ' = 3 d d x ( e x ) − d d x ( e 2 x ) y ' = 3 e x − 2 e 2 x For critical point y ' = 0 . 3 e x − 2 e 2 x = 0 ⇒ 3 e x − 2 e 2 x + 2 e 2 x = 0 + 2 e 2 x ⇒ 3 e x = 2 e 2 x ⇒ ln ( 3 e x ) = ln ( 2 e 2 x ) ⇒ ln ( 3 ) + ln ( e x ) = ln ( 2 e 2 x ) ⇒ ln ( 3 ) + ln ( e x ) = ln ( 2 ) +

4th Edition

ISBN: 9781319050740

Author: Jon Rogawski, Colin Adams, Robert Franzosa

Publisher: W. H. Freeman

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Question

Chapter 4.2, Problem 59E

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 58E

Chapter 4.2, Problem 60E

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Chapter 4 Solutions

Calculus: Early Transcendentals

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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 compares the minimum and maximum values of a given function in the given interval with critical and end points.

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