Question

The set of values of $x$ for which $f\left(x\right)=\cos x-$x is decreasing in

• A. $(-\infty ,0)$
• B. $(0,\infty )$
• C. $(-\infty ,\infty )$
• D. $\varnothing$

Answer 1

Answer: (C)

$(-\infty ,\infty )$

$f^{\prime }\left(x\right)=-\sin x-1$
$-1\le -\sin x\le 1$
$-2\le -\sin x-1\le 0$
$-2\le f^1\left(x\right)\le 0$
$f^1\left(x\right)\le 0$
So $f\left(x\right)$ is decreasing in $(-\infty ,\infty )$.