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 determine whether the function is increasing or decreasing, we compute its derivative:

\[ f'(x) = 2 - \sin x \]
Since the range of \( \sin x \) is \([-1, 1]\), we obtain:
\[ 1 \leq f'(x) \leq 3 \]

Thus, \( f'(x) > 0 \) for all real values of \( x \).

Conclusion:
The function is monotonically increasing for all real \( x \).