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

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

AP EAMCETAP EAMCET 2020

Solution:

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