Question

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

• A. $k>1$
• B. $k\ge 1$
• C. $k<1$
• D. $k\le 1$
• E. $k<-1$

Answer 1

The correct option is B $k\ge 1$

$f\left(x\right)=\sin x-kx-c$
$\Rightarrow f^{{}^{\prime }}\left(x\right)=\cos x-k$
$\therefore f$ decreases, if $f^{{}^{\prime }}\left(x\right)\le 0$
$\Rightarrow \cos x-k\le 0$
$\Rightarrow \cos x\le k$
So, for decreasing $k\ge 1$.