Question

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

• A. only (I) is true.
• B. only (II) is true.
• C. neither (I) nor (II) is true.
• D. both (I) and (II) are true.

Answer 1

The Correct Option is D

The correct answer is