For the function

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

Problem

For the function f(x)=∣x∣f(x)=|x|, what are the values of the one-sided derivatives at x=0x=0? (a) Lf′(0)=1,  Rf′(0)=1L f'(0) = 1,\; R f'(0) = 1 (b) Lf′(0)=0,  Rf′(0)=0L f'(0) = 0,\; R f'(0) = 0 (c) Lf′(0)=−1,  Rf′(0)=1L f'(0) = -1,\; R f'(0) = 1 (d) Lf′(0)=1,  Rf′(0)=−1L f'(0) = 1,\; R f'(0) = -1

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