Question

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

(i) π/2

(ii) 1

(iii) 2

(iv) -π/2

Answer 1

f(x) = sin 2x − x

⇒ f′(x) = 2 cos2x − 1

Clearly \(\frac{\sqrt3}{2}-\frac{\pi}{6}\) is the greatest value of f(x) and its least value is \(-\frac{\pi}{2}\).