Question

The function $\sin x–bx+c$will be increasing in the interval$(–\infty ,\infty )$, if

• A. $b\le 1$
• B. $b\le 0$
• C. $b<–1$
• D. $b\ge 0$

Answer 1

The correct option is C

$b<–1$

Explanation for correct option:

Monotonically Increasing Function

Let be $f\left(x\right)=\sin x–bx+c$

Now, $f\text{'}\left(x\right)=\cos x-b$

For increasing function, $f\text{'}\left(x\right)>0$

$$\begin{gathered} \Rightarrow \cos x-b>0 \\ \Rightarrow \cos x>b \end{gathered}$$

This is only possible if,

$b<-1$

Hence, the correct option is option(C).