Find the values of a for which the functionf ( x)= x - ax + 4 is … - Vidyadip

Question

Find the values of a for which the functionf $( x)= \sin x - ax + 4$ is increasing function on $R$.

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Answer

Given : $f(x)=\sin x-a x+4$
$f(x)=\cos x-a$
Given : $F(x)$ is increasing on $R$
$\Rightarrow f^{\prime}(x);0$
$\Rightarrow \cos x-a;0$
$\Rightarrow \cos x;a$
We know
$\operatorname{Cos} x;-1, \forall x \in R$
$\therefore a<-1$
$\Rightarrow a \in(-\infty,-1)$

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