ID: Class: 12Subject: MathTopic: Application of DerivativeType: McqYear: 2025
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
Official Solution
Correct Answer: is an increasing function
Explanation:
We differentiate $f(x)$ with respect to $x$:$$f'(x) = 2 - \sin x$$
We know that the range of the sine function is $-1 \le \sin x \le 1$.
This means that $f'(x)$ is always positive ($f'(x) > 0$) for all real values of $x$.
Since the first derivative $f'(x)$ is strictly positive for all $x$, the function $f(x) = 2x + \cos x$ is an increasing function throughout its domain.
This also rules out (A) and (B) because an increasing function has no local maxima or minima.
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