Question

The function $f\left(x\right)=\cos x-2px$ is monotonically decreasing for

• A. $p<\frac{1}{2}$
• B. $p>\frac{1}{2}$
• C. $p<2$
• D. $p>2$

Answer 1

Answer: (B)

$p>\frac{1}{2}$

$f\left(x\right)=\cos x-2px$
For monotonically decrea\sin g
$f^{\prime }\left(x\right)<0$
$-\sin x-2p<0$
$\sin x+2p>$
Now $\sin xϵ[-1,1]$
Hence
$1+2p>0$
$p>\frac{-1}{2}$ and
$-1+2p>0$
$p>\frac{1}{2}$.