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

Answer: (D)

both (I) and (II) are true.

Answer 2

The correct answer is