Let the f :R→R be defined by f (x) = 2x + cosx, then f :

Given f (x) = 2x + cosx if f:R→R

Applying the first derivative we ge

Applying the sum rule of differentiation and also the derivative of the constant is 0, so we get

Applying the power rule we get

⇒ f’(x)=2-sin x

Now we know, the maximum value of sin x is 1.

So f’(x)>0, ∀ x

Hence the function f is increasing function.

So the correct option is option D.