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: 25

Answer

See explanation.

Work Step by Step

Points where the tangent line is horizontal (and thus derivative is zero) are critical points, meaning the function is not differentiable. \[ x=\sqrt[3]{5} \text { and } x=0 \] Using the first derivative test $x=0$ is a double root, so $x=0$ is not a relative extremum. Use first derivative test $f^{\prime}(x)<0$ on the left and $f^{\prime}(x)>0$ on the right of $x=\sqrt[3]{5},$ so $\sqrt[3]{5}=x$ is a relative minimum.
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