Question

If $f(x)\,=kx\,-\,\cos \,x$ is monotonically increasing for all $x\in R,$ then

• A. $k>-1$
• B. $ k
• C. $k>1$
• D. $None\, of\, these$

Answer 1

Answer: (A)

$k>-1$

Answer 2

Given, $f(x)=kx-\cos x$ and $x\in R$
$f'(x)=k+\sin x$ Since, the function $f(x)$
is monotonically increase for all
$x\in R$ .
$\therefore$ $f'(x)>0,\,\,\,\forall \,\,\,\,x\in R$
$\Rightarrow$ $f'\left( \frac{\pi }{2} \right)>0$
$\Rightarrow$ $k+\sin \frac{\pi }{2}>0$
$\Rightarrow$ $k+1>0$
$\Rightarrow$ $k>-1$