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  4. If f(x) = kx - sin x is monotonically increasing, then

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Q. If $ f(x) = kx - sin \,x $ is monotonically increasing, then

MHT CETMHT CET 2007

Solution:

Since, $\,\,\, f(x)=k x-\sin x $ is monotonically increasing for all $x \in R$. Therefore,
$f'(x)>0$ for all $x \in R$
$\therefore \,\,\, f'(0)>0$
$\Rightarrow \,\, k-\cos 0 >0 $
$\Rightarrow \,\, k>1$