Which of the following functions is decreasing on $\left(0, frac{\pi}…

Question

Which of the following functions is decreasing on $\left(0,	frac{\pi}{2}ight)$?

Accepted Answer

B. $\cos x$

1. For $\cos x$: $f'(x)=-\sin x<0$ on $\left(0,	frac{\pi}{2}ight)$, so it is decreasing.
2. For $\sin x$: $f'(x)=\cos x>0$, increasing.
3. For $	an x$: $f'(x)=\sec^2 x>0$, increasing.
4. For $x^2$: $f'(x)=2x>0$, increasing.
_Source: syllabus Mathematics Ch 6 "Application of Derivatives", p.12_

Answer

$	an x$

Answer

$\sin x$

Answer

$x^2$

Which of the following functions is decreasing on $\left(0,\tfrac{\pi}{2}\right)$?

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