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  4. The function f(x) = sin x - kx - c, where k and c are constants, decreases always when

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Q. The function $f(x) = \sin x - kx - c$, where $k$ and $c$ are constants, decreases always when

VITEEEVITEEE 2017

Solution:

$f(x)=\sin x-k x -c$
$\Rightarrow f'(x)=\cos x-k$
$\therefore f \text { decreases, if } f(x) \leq 0$
$\Rightarrow \cos x-k \leq 0$
$\Rightarrow \cos x \leq k$
So, for decreasing $k \geq 1$.