Q34 of 105 Page 17

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 ().

Prove that the function f given by f(x) = x³ – 3x² + 4x is strictly increasing on R ?

33 Prove that the function f(x) = cos x is :

i. strictly decreasing on (0, π)

ii. strictly increasing in (π, 2π)

iii. neither increasing nor decreasing in (0, 2 π)

Find the value(s) of a for which f(x) = – ax is an increasing function on R ?

Find the values of b for which the function f(x) = sin x – bx + c is a decreasing function on R ?