Question

If $f\left(x\right)=kx-\sin x$ is monotonically increasing, then

• A. $k>1$
• B. $k>-1$
• C. $k<1$
• D. $k<-1$

Answer 1

The correct option is A $k>1$

Since $f\left(x\right)=kx-\sin x$ is monotonically increasing for all $X\in R$. Therefore

$f^{\prime }\left(x\right)>0$ for all $x\in R$

$\therefore$ $f^{\prime }\left(0\right)>0$

$\Rightarrow$ $k-\cos 0>0$

$\Rightarrow$ $k-1>0$

$\Rightarrow$ $k>1$