For the function \(f(x) = \sin x + 3x - \frac{2}{\pi}(x^2 + x), \quad x \in \left[0, \frac{\pi}{2}\right],\)consider the following two statements:
1. \( f \) is increasing in \( \left(0, \frac{\pi}{2}\right) \).
2. \( f' \) is decreasing in \( \left(0, \frac{\pi}{2}\right) \).
Between the above two statements
1. \( f \) is increasing in \( \left(0, \frac{\pi}{2}\right) \).
2. \( f' \) is decreasing in \( \left(0, \frac{\pi}{2}\right) \).
Between the above two statements
- only (I) is true.
- only (II) is true.
- neither (I) nor (II) is true.
- both (I) and (II) are true.
The Correct Option is D
Solution and Explanation
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