Explanation Given information: The graph of f ′ ( x ) is redrawn as shown in Figure 1 . Concept used: If a function f ( x ) has a critical point as x = c then, f ( c ) is a local maximum if f ′ ( x ) changes sign from positive to negative at x = c . f ( c ) is a local minimum if f ′ ( x ) changes sign from negative to positive at x = c . Calculation: Figure 1 represents the graph of the derivative of the function f ( x ) that is f ′ ( x ) . The critical point is defined as the point or the value of x such that f ′ ( x ) = 0 . From the graph of the function f ′ ( x ) it observed that curve intersects the x -axis or touches the x -axis at the point ( − 1 , 0 ) , ( 0.5 , 0 ) and ( 2 , 0 ) . This implies that the critical points for the function f ( x ) are x = − 1 , x = 0.5 and x = 2 . The critical points divide the domain of the function into four intervals as ( − ∞ , − 1 ) , ( − 1 , 0.5 ) , ( 0.5 , 2 ) and ( 2 , ∞ ) . The behavior in value of the function f ′ ( x ) is expressed in Table 1 as shown below, Interval Sign of f ′ ( x ) ( − ∞ , − 1 ) Positive ( − 1 , 0.5 ) Positive ( 0

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 4.3, Problem 18E

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The critical points for the function f(x) and classify the nature of the critical points.

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Chapter 4.3, Problem 17E

Chapter 4.3, Problem 19E

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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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The critical points for the function f ( x ) and classify the nature of the critical points.

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The critical points for the function f ( x ) and classify the nature of the critical points.

Solution Summary: The author explains the critical points for the function f(x) and classifies their nature.

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To find: The critical points for the function f(x) and classify the nature of the critical points.

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Chapter 4 Solutions

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The critical points for the function f(x) and classify the nature of the critical points.