Explanation Given: f ( x ) = x 3 + 3 x 2 + 6 x First of all let us consider f ( 0 ) = 0 . Therefore, the function has at least one real root. To prove that this the only root, we proceed with contradiction rule. That is let us the function has another real root say x = a. Since the given polynomial function is continuous and differentiable for all real x and according to Rolle’s Theoremthat there exist a real number c between 0 and a such thatf’(c) = 0

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topic…

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Chapter 4.2, Problem 62E

To determine

To prove that f(x)=x3+3x2+6x has precisely one real root.

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Chapter 4.2, Problem 61E

Chapter 4.2, Problem 63E

Chapter 4 Solutions

Calculus - Standalone book

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 prove that f ( x ) = x 3 + 3 x 2 + 6 x has precisely one real root.

Solution Summary: The author concludes that the given polynomial function can have only one real root.

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To prove that f(x)=x3+3x2+6x has precisely one real root.

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