Let . Which of the following correctly describes the sign of for all in the interval…

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

Problem

Let g(x)=cos⁡xg(x)=\cos x. Which of the following correctly describes the sign of g′(x)g'(x) for all xx in the interval (0,π)(0,\pi)? (a) g′(x)g'(x) is positive for all xx\;in (0,π)(0,\pi) (b) g′(x)g'(x) changes sign within (0,π)(0,\pi) (c) g′(x)g'(x) is negative for all xx\;in (0,π)(0,\pi) (d) g′(x)g'(x) is positive on (0,π2)(0,\tfrac{\pi}{2}) and negative on (π2,π)(\tfrac{\pi}{2},\pi)

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