Show that f(x) = – x sin x is an increasing function on (0, π/2) ?

We have,

f(x) = – x sinx

f ’(x) = 2x – sin x – x cos x

Now,

x ()

⇒ 0 sin x 1, 0 cos x 1,

⇒ 2x–sin x –x cos x > 0

⇒ f ’(x) ≥ 0

Hence,f(x) is an increasing function on ().