Which of the following functions is decreasing on $(0, \frac{\pi}{2})$?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → $\cos x$ ##
In the interval $(0, \frac{\pi}{2})$, $f(x) = \cos x$
$\Rightarrow f'(x) = -\sin x$
which gives $f'(x) < 0$ in $(0, \frac{\pi}{2})$.
Hence, $f(x) = \cos x$ is decreasing in $(0, \frac{\pi}{2})$.