Define r(x)={(x+2)3,x<−1,x2−1,−1≤x≤2,(x−2)3+5,x>2.r(x)=\begin{cases} (x+2)^{3},& x<-1,\\ x^{2}-1,& -1\le x\le 2,\\ (x-2)^{3}+5,& x>2. \end{cases}…

Mathematics

Problem

Define r(x)={(x+2)3,x<−1,x2−1,−1≤x≤2,(x−2)3+5,x>2.r(x)=\begin{cases} (x+2)^{3},& x<-1,\\ x^{2}-1,& -1\le x\le 2,\\ (x-2)^{3}+5,& x>2. \end{cases} List all xx-values at which rr has a relative extremum on R\mathbb{R} and specify whether each is a relative maximum or a relative minimum.

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