Explanation Given information: f ( x ) = x ( x 2 − 4 ) Calculation: Consider f ( x ) = x ( x 2 − 4 ) Make a table of values x − 2 − 1 0 1 2 f ( x ) 0 9 0 − 3 0 Draw the graph by hand as follows: Find the Critical points by equating first derivative to zero. f ( x ) = x ( x 2 − 4 ) f ' ( x ) = 3 x 2 − 4 = 0 x = ± 2 / 3 Then, consider the intervals ( − ∞ , − 2 / 3 ) , ( − 2 / 3 , 2 / 3 ) , ( 2 / 3 , ∞ ) . From each interval take a test point ( − ∞ , − 2 / 3 ) ⇒ f ' ( − 5 ) > 0 increasing ( − 2 / 3 , 2 / 3 ) ⇒ f ' ( − 2 ) < 0 decreasing ( 2 / 3 , ∞ ) ⇒ f ' ( 2 ) > 0 increasing The sign diagram of derivative:

14th Edition

ISBN: 9781464151088

Author: Associate Professor Laura Taalman, Peter Kohn

Publisher: W.H. Freeman & Company

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Chapter 3.2, Problem 62S

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Chapter 3.2, Problem 61S

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The graph of the given function, to make sign diagrams, to find undefined points and to describe behavior of the function.

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To sketch: The graph of the given function, to make sign diagrams, to find undefined points and to describe behavior of the function.

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To sketch: The graph of the given function, to make sign diagrams, to find undefined

points and to describe behavior of the function.