Consider the piecewise function g(x)= cases x, & x 0, 2x, & x>0

MATHEMATICS · Subjective · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

Consider the piecewise function g(x)={x,x≤0,2x,x>0.g(x)=\begin{cases}x, & x\le 0,\\2x, & x>0.\end{cases} Describe why x=0x=0 is a critical number of gg and simultaneously not a local maximum or minimum.

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