Browse Questions

# Which of the following functions is decreasing on $\bigg(0,\frac{1}{2}\bigg)$

$(A)\;\sin 2x\quad(B)\;\tan x\quad(C)\;\cos x\quad(D)\;\cos 3x$

Toolbox:
• Let $f(x)$ be a function defined on $(a,b)$ if $f'(x) <0$ for all $x \in (a,b)$ except for a finite number of points where $f'(x)=0$, then $f(x)$ is decreasing on $(a,b)$
Step 1
$0, \large\frac{\pi}{2}$ is the I quadrant
The value of $\cos x$ ranges from 1 to 0 in the I quadrant.
i.e., $\cos 0=1 : \cos \large\frac{\pi}{4}=\large\frac{1}{\sqrt 2}, \cos \large\frac{\pi}{3}=\large\frac{1}{2}\: and \: \cos \large\frac{\pi}{2}=0$
hence it is clear that $\cos x$ decreases in the interval $\bigg( 0, \large\frac{\pi}{2} \bigg).$
Hence the correct option is C