alleryThe function $f(x)=\cos x$ is decreasing on the interval
A$(\pi,2\pi)$
B$\left(\tfrac{\pi}{2},\pi\right)$ only
C$(0,2\pi)$
D$(0,\pi)$
Answer & Solution
Correct answer: D. $(0,\pi)$
1. $f'(x)=-\sin x$.
2. On $(0,\pi)$, $\sin x>0$, so $f'(x)<0$ (decreasing).
3. On $(\pi,2\pi)$, $\sin x<0$, so $f'(x)>0$ (increasing), ruling out A.
_Source: syllabus Mathematics Ch 6 "Application of Derivatives", p.8_
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