Explanation Given: f ( x ) = x + | 2 x + 1 | In this function, we must separately solve the absolute terms. Then | 2 x + 1 | = 0 2 x + 1 = 0 x = − 1 2 The intervals are defined around the zeros. Therefore, x < − 1 2 ; x = − 1 2 ; x > − 1 2 Now, we must evaluate the behavior of the function for each interval. For the interval, x < − 1 2 x + | 2 x + 1 | ⇒ x + ( − 2 x − 1 ) = − x − 1 For the interval, x = − 1 2 x + | 2 x + 1 | ⇒ − 1 2 + ( − 2 ( − 1 2

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ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 4.2, Problem 14E

To determine

To find all the critical points of the function f(x)=x+|2x+1|

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Chapter 4.2, Problem 13E

Chapter 4.2, Problem 15E

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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To find all the critical points of the function f ( x ) = x + | 2 x + 1 |

Solution Summary: The author explains that the critical point for the given function occurs at x=-12. The intervals are defined around the zeros.

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To find all the critical points of the function f(x)=x+|2x+1|

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