Question

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

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

Answer 1

The correct option is A

$k>1$

Explanation for correct option:

Find the relation:

Given,

$f\left(x\right)=kx–\sin x$

Differentiated the given function with respect to $x$,

$f’\left(x\right)=k–\cos x\left[\because \frac{d}{dx}\left(sinx\right)=cosx\right]$

Since, the function is monotonically increasing,

$$\begin{gathered} f\text{'}\left(x\right)>0 \\ \Rightarrow k–\cos x>0 \end{gathered}$$

At $x=0$, we get

$$\begin{gathered} k>\cos 0 \\ \Rightarrow k>1\left[\because \cos x\in [-1,1]\right] \end{gathered}$$

Hence, the correct option is A.