Maxima Minima

To solve the problem, we need to evaluate different aspects of the function within the interval .

1. Finding : To find the derivative of the function, start by using the derivatives of the trigonometric functions:
   • (chain rule applied)
   Thus, the derivative is:

Statement (A) is correct.

2. Finding critical points: Critical points occur where :

This gives us two equations:

Both critical points and are in the interval. Thus, statement (B) is correct.

3. Finding the maximum and minimum values: Use critical points and boundary points:

• ,
• ,
• ,

The maximum value is , not 2, so statement (D) is correct, but statement (C) is incorrect.

Therefore, the correct answer is: (A), (B), and (D) only.

The given function attains its maximum value at points and . At these points:

Since both points yield the same maximum value:

Simplify the equation:

Using the condition :

Substitute and into . At point :

Thus, the maximum value of is 50.