Explanation Given: f ( x ) = x 4 + 5 x 3 + 4 x We proceed with contradiction rule to prove that the function has no root. First of all let us consider f ( 0 ) = 0 and suppose that there exists a c > 0 such that f(c) = 0. Then, f(0) =f(c) = 0 and Rolle’s Theorem guarantees that there exist a d ∈ ( 0 , c ) such that f’(d) = 0 Now, f ' ( x ) = 4 x 3 + 15 x 2 + 4 > 4 for all x > 0

4th Edition

ISBN: 9781319323394

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 4.2, Problem 67E

To determine

To prove that f(x)=x4+5x3+4x has no root c satisfying c > 0.

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Chapter 4.2, Problem 66E

Chapter 4.2, Problem 68E

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Chapter 4 Solutions

CALCULUS W/SAPLING ACCESS >IC<

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