153.

Show that f (x) = tan ^-1 (sin x + cos x) is a strictly increasing function in the interval 

Determine whether  is increasing or decreasing for 

Prove that the function f given by f(x) = log cos x is strictly decreasing on  and strictly increasing on 

Find the value of a for which the function f (x) = x³ – 2ax + 6 is increasing for x > 0.

Show that  is an increasing function of x throughout its domain.

Find the values of x for which y = [x ( x – 2)]² is an increasing function.