Question

Find the values of 'a' for which the function f(x) = sin x − ax + 4 is increasing function on R.

Answer 1

$$\begin{gathered} f\left(x\right)=\sin x-ax+4 \\ f\text{'}\left(x\right)=\cos x-a \\ \text{Given:}\mathit{\text{f}}\text{(}\mathit{\text{x}}\text{) is increasing on}\mathit{\text{R}}\text{.} \\ \Rightarrow f\text{'}\left(x\right)>0 \\ \Rightarrow \cos x-a>0 \\ \Rightarrow \cos x>a \\ \text{We know,} \\ \cos x\ge -1,\forall x\in R \\ \Rightarrow a<-1 \\ \Rightarrow a\in \left(-\infty ,-1\right) \end{gathered}$$