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 ().