The function f(x) = sin x (1 + cos x) has a maximum value on [0, π] equal to:

The function f(x) = sin x (1 + cos x) has a maximum value on [0, π] equal to:

• A. 3√3/4
• B. √3/2
• C. 1
• D. √3/4

Answer: A) 3√3/4

Explanation: f'(x) = cos x (1 + cos x) − sin² x = cos x + cos² x − (1 − cos² x) = 2cos² x + cos x − 1 = (2cos x − 1)(cos x + 1). On [0, π], cos x = 1/2 gives x = π/3. f(π/3) = (√3/2)(1 + 1/2) = 3√3/4. f(0) = 0, f(π) = 0. Max = 3√3/4.