Find the values of b for which the function


Find the values of $b$ for which the function $f(x)=\sin x-b x+c$ is a decreasing function on $R$ ?


We have,

$f(x)=\sin x-b x+c$

$f^{\prime}(x)=\cos x-b$

Given that $f(x)$ is on decreasing function on $R$

$\therefore \mathrm{f}^{\prime}(\mathrm{x})<0$ for all $\mathrm{x} \in \mathrm{R}$

$\Rightarrow \cos x-b>0$ for $a l l x \in R$

$\Rightarrow b<\cos x$ for all $x \in R$

But the last value of $\cos x$ in 1

$\therefore \mathrm{b} \geq 1$

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