Question

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

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

Answer 1

Answer: (B)

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