Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 3 - The Derivative In Graphing And Applications - 3.4 Absolute Maxima And Minima - Exercises Set 3.4 - Page 223: 25

Answer

$${\text{no maximum or minimum}}$$

Work Step by Step

$$\eqalign{ & f\left( x \right) = 2{x^3} - 6x + 2;\,\,\left( { - \infty , + \infty } \right) \cr & {\text{The function is a polynomial }} \cr & {\text{Since }}f(x){\text{ has odd }}\,{\text{degree we have that}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\mathop {\lim }\limits_{x \to + \infty } f\left( x \right){\text{ and }}\mathop {\lim }\limits_{x \to - \infty } f\left( x \right) \cr & {\text{have opposite signs }}\left( {{\text{one is + }}\infty {\text{ and the other is }} - \infty } \right),{\text{ so there are no}} \cr & {\text{absolute extrema}}{\text{.}} \cr} $$
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