Mathematics

Mathematics

Problem

The piecewise function gg is defined by g(x)={x3+3x2,x<0,−x3+3x,x≥0.g(x)=\begin{cases}x^{3}+3x^{2}, & x<0,\\-x^{3}+3x, & x\ge 0.\end{cases} Identify every interval on which gg is concave down and list the xx-values of any points of inflection.

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