The value of ' $k$ ' for which the function $f(x)=k(x+\sin x)+k$ is increasing, is equal to

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Aicharya · Accepted Answer

Given function $f(x)=k(x+\sin x)+k$ So, $\quad f^{\prime}(x)=k(1+\cos x)$ $\because f(x)$ is an increasing function, so $\begin{aligned} & f^{\prime}(x) \geq 0 \ & \Rightarrow \quad k(1+\cos x) \geq 0 \ & \Rightarrow \quad k > 0 \quad\{\because 1+\cos x \geq 0\} \ \end{aligned}$

The value of ' \(k\) ' for which the function \(f(x)=k(x+\sin x)+k\) is increasing, is equal to

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