Consider the following statements

MATHEMATICS · Subjective · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

Consider the following statements. Statement I: If f(x)=⌊x⌋(sin⁡x+cos⁡x−1)f(x)=\lfloor x\rfloor(\sin x+\cos x-1), where ⌊⋅⌋\lfloor\cdot\rfloor denotes the greatest integer function, then f′(x)=⌊x⌋(cos⁡x−sin⁡x)f'(x)=\lfloor x\rfloor(\cos x-\sin x) for every integer xx. Statement II: f′(x)f'(x) does not exist for any integer xx.

Related theory

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