What is the length of the longest interval in which the function \( f(x) = 2\cos^2 x - 1 \) is decreasing ?
- A. 2\pi
- B. \pi
- C. \frac{\pi}{2} ✓
- D. \frac{\pi}{4}
Correct Answer: C. \frac{\pi}{2}
Explanation
The function simplifies to \( \cos 2x \), whose derivative is \( -2\sin 2x \). It is decreasing when \( \sin 2x > 0 \), which happens over intervals of length \( \frac{\pi}{2} \).
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