Question

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

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

Answer 1

Answer: (C)

Is an increasing function

$f\left(x\right)=2x+\cos x$

Now,

$f^{\prime }\left(x\right)=2-\sin x$,

Now, $f^{\prime }\left(x\right)$ will be positive for all value of $x$.

i.e. $f^{\prime }\left(x\right)>0\forall x\in R$

So, the function is increasing for all value of $x$ and it does not have any defined maximum and minimum.

Hence, C is correct.