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

Problem

For f(x)=arccos⁡(x)f(x)=\arccos(x) defined on (−1,1)(-1,1), which statement about f′(x)f'(x) is most accurate? (a) f′(x)f'(x) is zero only at x=0x=0 and negative elsewhere in (−1,1)(-1,1). (b) f′(x)f'(x) changes sign exactly once in (−1,1)(-1,1) at x=12x=\dfrac{1}{\sqrt{2}}. (c) f′(x)f'(x) is negative for all xx in (−1,1)(-1,1). (d) f′(x)f'(x) is positive for all xx in (−1,1)(-1,1).

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