If , where and denote greatest integer and fractional part of ,…

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

Problem

If f(x)={[cos⁡πx],x≤12{x}−1,x>1f(x) = \begin{cases} [\cos \pi x], & x \le 1 \\ 2\{x\} - 1, & x > 1 \end{cases}, where [⋅][\cdot] and {⋅}\{\cdot\} denote greatest integer and fractional part of xx, then (1) f′(1−)=2f'(1^-) = 2 (2) f′(1+)=2f'(1^+) = 2 (3) f′(1−)=−2f'(1^-) = -2 (4) f′(1+)=0f'(1^+) = 0

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