AP

MATHEMATICS · Single correct · AP · AP Precalculus · Trigonometric and Polar Functions · Trigonometric and Polar Functions

Problem

Let f(x)=xcos⁡−1(sin⁡(−∣x∣))f(x) = x \cos^{-1}(\sin(-|x|)), x∈(−π2,π2)x \in \left(-\frac{\pi}{2}, \frac{\pi}{2}\right) then (a) f′(0)=−π2f'(0) = -\frac{\pi}{2} (b) f′(x)f'(x) is not defined at x=0x = 0 (c) f′(x)f'(x) is increasing in (−π2,0)\left(-\frac{\pi}{2}, 0\right) and f′(x)f'(x) is decreasing in (0,π2)\left(0, \frac{\pi}{2}\right) (d) f′(x)f'(x) is decreasing in (−π2,0)\left(-\frac{\pi}{2}, 0\right) and f′(x)f'(x) is increasing in (0,π2)\left(0, \frac{\pi}{2}\right)

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