Question

If $f(x)=kx-sinx$ is monotonically increasing, then

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

Answer 1

Answer: (A)

Since, $f(x)=kx-\sin x$ is monotonically increasing for all $x\in R$. Therefore,
$f^{\prime }(x)>0$ for all $x\in R$
$\therefore f^{\prime }(0)>0$
$\Rightarrow k-\cos 0>0$
$\Rightarrow k>1$