Consider the piecewise function f(x)= cases (x+2)^ 2/3 ,&x 0 ^ 2 ,&x>0 cases

MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

Consider the piecewise function f(x)={(x+2)2/3,x≤0x2,x>0.f(x)=\begin{cases}(x+2)^{2/3},&x\le 0\\x^{2},&x>0\end{cases}. For which of the following xx-values does f′(x)f'(x) fail to exist? (a) x=−2 onlyx=-2\text{ only} (b) x=0 onlyx=0\text{ only} (c) x=−2 and x=0x=-2\text{ and }x=0 (d) x=−2 and x=2x=-2\text{ and }x=2

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