The left-hand derivative of at

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

Problem

The left-hand derivative of f(x)=⌊x⌋sin⁡(πx)f(x)=\lfloor x\rfloor\sin(\pi x) at x=kx=k, where kk is an integer, is (1) (−1)k(k−1)π(-1)^k(k-1)\pi (2) (−1)k−1(k−1)π(-1)^{k-1}(k-1)\pi (3) (−1)kπ(-1)^k\pi (4) (−1)k−1π(-1)^{k-1}\pi

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