Let h(x)= cases |x+1|,&x2 cases

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

Problem

Let h(x)={∣x+1∣,x<−1(x+1)1/3,−1≤x≤231/3−∣x−2∣,x>2.h(x)=\begin{cases}|x+1|,&x<-1\\(x+1)^{1/3},&-1\le x\le 2\\3^{1/3}-|x-2|,&x>2\end{cases}. At which xx-value(s) is hh continuous but not differentiable? (a) x=−1x=-1 (b) x=−1 and x=2x=-1 \text{ and } x=2 (c) x=2x=2 (d) h is differentiable at every x where it is continuoush \text{ is differentiable at every } x \text{ where it is continuous}

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