If for and denotes the greatest integer less than or equal to

MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions

Problem

If f(x)=sin⁡{π3[x]−x2}f(x) = \sin \left\{ \frac{\pi}{3} [x] - x^2 \right\} for 2<x<32 < x < 3 and [x][x] denotes the greatest integer less than or equal to xx , then f′(π/3)f'(\sqrt{\pi/3}) is equal to (1) π/3\sqrt{\pi/3} (2) −π/3-\sqrt{\pi/3} (3) −π-\sqrt{\pi} (4) None of these

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