Question

The maximum value of y = sin2x - x on the interval [-π/2, π/2] is

(1) π/2

(2) 1

(3) 2

(4) -π/2

Answer 1

The correct option is (1) \(\frac{\pi}{2}\)

f(x) = sin2x – x

⇒ f′(x) = 2 cos2x – 1

Therefore, f′(x) = 0

Clearly, \(\frac{\pi}{2}\) is the greatest value and -\(\frac{\pi}{2}\) is the least.