Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 3 - Applications of Differentiation - 3.1 Maximum and Minimum Values - 3.1 Execises: 69

Answer

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Work Step by Step

Prove that the function $f(x) = x^{101} + x^{51} + x + 1$ has no minimum or maximum values. $f'(x) = 101x^{100} + 51x^{50} + 1$ Because $f'(x)$ is a polynomial with positive coefficients and even powers, it is always positive. Thus $f(x)$ is always increasing. If $f(x)$ is always increasing, it can have no maximum or minimum values.
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