Question

Interval of $k$ for which $f\left(x\right)=\sin x-\cos x-kx+b$ is decreasing for all real values of $x$.

• A. $(-\infty ,\sqrt{2}]$
• B. $[\sqrt{2},\infty )$
• C. $(0,\infty )$
• D. $[-\sqrt{2},\sqrt{2}]$

Answer 1

The correct option is B $[\sqrt{2},\infty )$

$f^{\prime }\left(x\right)=\cos x+\sin x-k\le 0$

$k\ge \sin x+\cos x$

$k\ge \sqrt{2}$