Explanation Given information: A function is given as, f ( x ) = x 2 1 − x 2 . Concept used: Critical Point: a number c in the domain of f is called a critical point if either f ' ( c ) = 0 or f ' ( c ) does not exists. Calculation: Given function is, f ( x ) = x 2 1 − x 2 . Using product rule, d ( u v ) d x = v d u d x + u d v d x So, f ' ( x ) = 1 − x 2 × 2 x + x 2 × ( 1 2 ) ( 1 − x 2 ) 1 2 − 1 × ( 0 − 2 x ) ⇒ f ' ( x ) = 2 x × ( 1 − x 2 )

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Question

Chapter 4.2, Problem 13E

To determine

All critical points of given function.

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Chapter 4.2, Problem 12E

Chapter 4.2, Problem 14E

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Chapter 4 Solutions

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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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All critical points of given function.

Solution Summary: The author explains that a number c in the domain of f is called critical point if either F'(c)=0 or

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