The absolute minimum value of f(x) = 2 sin x + cos 2x on [0, π/2] is:

The absolute minimum value of f(x) = 2 sin x + cos 2x on [0, π/2] is:

• A. 1
• B. 3/2
• C. 2
• D. 0

Answer: A) 1

Explanation: f'(x) = 2 cos x - 2 sin 2x = 2 cos x(1 - 2 sin x) = 0. In [0, π/2], critical points are x = π/2, x = π/6. f(0) = 1, f(π/6) = 1.5, f(π/2) = 1. Absolute minimum is 1.