# Let the $f:R\rightarrow R$ be defined by $f(x)=2x+\cos x,$then

$\begin{array}{1 1} (A)\;\text{has a minimum at$x=\pi$} \\ (B)\;\text{has a maximum,at x=0}\\(C)\;\text{is a decreasing function} \\ (D)\;\text{is an increasing function}\end{array}$

Toolbox:
Step 1
$f(x)=2x+ \cos x$
differentiating w.r.t $x$
$f'(x)=2- \sin x$
But we know the range of $\sin \theta$ is $-1 < x < 1$
hence this implies that
$f'(x) > 0$ for all values of $x$
Hence it is an increasing function.