Consider the piecewise function f(x)= cases 3-x, & x -1

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

Problem

Consider the piecewise function f(x)={3−x,x≤−1,x2,−1<x<2,∣x−2∣+2,x≥2.f(x)=\begin{cases} 3-x, & x\le -1,\\ x^2, & -1<x<2,\\ |x-2|+2, & x\ge 2. \end{cases} For which value(s) of xx does ff fail to be differentiable? (a) x=−1x=-1 only (b) x=−1 and x=2x=-1 \text{ and } x=2 (c) x=2x=2 only (d) ff is differentiable for all real xx

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