Question

Let the $f:R\to R$ be defined by
$f\left(x\right)=2x+cosx$, then $f\left(x\right)$ :

• A. is a decreasing function
  
• B. has a minimum at $x=\pi$
• C. is an increasing function
  
• D. has a maximum at $x=0$
  

Answer 1

The correct option is C is an increasing function


Given: $f\left(x\right)=2x+\cos x$
Differentiating above eq. w.r.t., $x$,

$\Rightarrow f^{\prime }\left(x\right)=2-\sin x>0\forall x$

$[\because -1\le \sin x\le 1]$

Hence, $f^{\prime }\left(x\right)>0$

$\therefore f\left(x\right)$ is an increasing function.

Hence, option (d) is correct.