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

Find the intervals in which f(x) = (x + 2)e^–x is increasing or decreasing ?

Show that the function f given by f(x) = 10^x is increasing for all x ?

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) = log cos x is strictly increasing on (–π/2, 0) and strictly decreasing on (0, π/2) ?