Explanation Given information: f ( x ) = x 2 − x + 100 Calculation: Consider f ( x ) = x 2 − x + 100 Make a table of values x − 10 − 5 − 2 0 5 10 f ( x ) 190 130 0.25 100 130 190 Draw the graph by hand as follows: Find the Critical points by equating first derivative to zero. f ( x ) = x 2 − x + 100 f ' ( x ) = 2 x − 1 = 0 x = 0.5 Critical points is x = 0.5 Then, consider the intervals ( − ∞ , 0.5 ) , ( 0.5 , ∞ ) . From each interval take a test point ( − ∞ , 0.5 ) ⇒ x = 0 ⇒ f ' ( 0 ) < 0 decreasing ( 0.5 , ∞ ) ⇒ x = 1 ⇒ f ' ( 1 ) > 0 increasing The sign diagram of derivative:

14th Edition

ISBN: 9781464140051

Author: TAALMAN, Laura, Kohn, Peter

Publisher: W. H. Freeman

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Chapter 3.2, Problem 58S

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

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Chapter 3.2, Problem 57S

Chapter 3.2, Problem 59S

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Chapter 3 Solutions

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Ch. 3.1 - Prob. 1TB Ch. 3.1 - Prob. 0C Ch. 3.1 - Prob. 1C Ch. 3.1 - Prob. 2C Ch. 3.1 - Prob. 3C Ch. 3.1 - Prob. 4C Ch. 3.1 - Prob. 5C Ch. 3.1 - Prob. 6C Ch. 3.1 - Prob. 7C Ch. 3.1 - Prob. 8C

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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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Chapter 3 Solutions

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

points and to describe behavior of the function.