Question

If $f(x) = 2x + \cos x$, then $f(x)$ :

• A. has a maxima at $x = \pi$
• B. has a minima at $x = \pi$
• C. is an increasing function
• D. is a decreasing function

Hint:

To determine if a function is increasing or decreasing, check the sign of its derivative. If the derivative is positive, the function is increasing.

Answer 1

The Correct Option is C

To check whether the function is increasing or decreasing, we find its derivative: \[ f'(x) = 2 - \sin x \] Since $\sin x$ ranges from -1 to 1, we have $1 \leq f'(x) \leq 3$. Therefore, $f'(x)>0$ for all $x$, meaning that the function is always increasing.