Question:
If $f(x) = 2x + \cos x$, then $f(x)$ :
If $f(x) = 2x + \cos x$, then $f(x)$ :
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To determine if a function is increasing or decreasing, check the sign of its derivative. If the derivative is positive, the function is increasing.
Updated On: Jun 16, 2025
- has a maxima at $x = \pi$
- has a minima at $x = \pi$
- is an increasing function
- is a decreasing function
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The Correct Option is C
Solution and Explanation
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.
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