Prove that the function f given by f(x) = log cos x is strictly increasing on (–π/2, 0) and strictly decreasing on (0, π/2) ?

Prove that the function f given by f(x) = x – [x] is increasing in (0, 1) ?

Prove that the following function is increasing on r?

i. f(x) = 3x⁵ + 40x³ + 240x

ii. f(x) = 4x³ – 18x² + 27x – 27

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)