Mathematics

Mathematics

Problem

Consider the piecewise-defined function g(x)={x2,x≤1,2x−1,x>1.g(x)=\begin{cases} x^{2}, & x\le 1,\\ 2x-1, & x>1. \end{cases} Determine whether gg has a local maximum, a local minimum, or neither at x=1x=1.

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