Let for all real

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

Problem

Let f(x)=⌊x⌋+∣x−1∣f(x)=\lfloor x \rfloor + |x-1| for all real xx, where ⌊x⌋\lfloor x \rfloor denotes the greatest integer less than or equal to xx. In the open interval (0,4)(0,4), the number of points at which ff is not differentiable is (a) 4 (b) 3 (c) 2 (d) infinitely many

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