Question

If $f\left(x\right)=kx-\cos x$ is monotonically increasing for all $x\in R$, then

• A. $K>–1$
• B. $K<1$
• C. $K>1$
• D. None of these

Answer 1

The correct option is A

$K>–1$

Explanation for correct option:

Find the value of $k$:

Given,

$f\left(x\right)=kx–\cos x$

Differentiated the given function with respect to $x$.

$f\text{'}\left(x\right)=k+\sin x$

Since the function is monotonically increasing for all $x\in R,f’\left(x\right)>0$, so

$$\begin{gathered} f\text{'}(\pi /2)>0 \\ \Rightarrow k+\sin (\pi /2)>0 \\ \Rightarrow k+1>0 \\ \Rightarrow k>-1 \end{gathered}$$

Hence, the correct option is A.