Q. If $f(x) = kx - \sin x$ is monotonically increasing, then
A) $k > 1$
B) $k > - 1$
C) $k < 1$
D) $k < - 1$
Explanation
(a)
Since,$f(x) = kx - \sin x$is monotonically increasing for all $x \in R.$Therefore,
$f^{'}(x) > 0$for all $x \in R$
$\Rightarrow K - \cos{x > 0}$
$\Rightarrow K > \cos x$
$\Rightarrow K > 1\ \lbrack\therefore maximum\ value\ of\cos{x\ is\ 1\rbrack}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.