Question

The function $f(x)=\cos x$ is strictly decreasing on

• A. $[0,\pi ]$
• B. $[0,\pi )$
• C. $(0,\pi ]$
• D. $(0,\pi )$

Answer 1

Answer: (D)

Let $f(x)=\cos x$
$\Rightarrow f^{\prime }(x)=-\sin x$
For strictly decreasing, $f^{\prime }(x)<0\Rightarrow -\sin x<0$
$\Rightarrow \sin x>0$, which is true for all $x\in (0,\pi )$