Use any method to find the relative extrema of [tex]|1+\sqrt[3]{x}|[/tex].(adsbygoogle = window.adsbygoogle || []).push({});

I get the following [tex] |1+\sqrt[3]{x}| = \left\{\begin{array}{cc} 1+\sqrt[3]{x}, & \mbox{if} x >-1 \\ -1-\sqrt[3]{x}, & \mbox{if} x<-1\end{array}\right[/tex]

Using the first derivative test, I get [tex] f'(x) = \frac{1}{3x^{2/3}} \mbox{and} -\frac{1}{3x^{2/3}}[/tex]. These suggest that there is a relative extremum at x=0 but not at x=-1, actually it is an inflection point at x=0. What is next? Maybe I am confused about absolute values! I think I have the function piece wise ok.Please help. Thanks.

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# Relative extrema of|f(x)|

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