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 - 3.2 Analysis Of Functions II: Relative Extrema; Graphing Polynomials - Exercises Set 3.2 - Page 206: 38

Answer

No relative extrema.

Work Step by Step

First derivative \[ x^{-2 / 3}+2=f^{\prime}(x) \] Critical points (zeros of first derivative or point where the first derivative does not exist): \[ x=0 \] No relative extrema $f^{\prime}(x)>0$ on the right of $x=0$ on the left. Since no change in the first derivative exists, it is not a relative extrema.
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