Ask Questions, Get Answers

Home  >>  CBSE XII  >>  Math  >>  Application of Derivatives

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

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

1 Answer

  • 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
answered Aug 11, 2013 by thanvigandhi_1