Strictly increasing functions and strictly decreasing functions

Define the strictly increasing function and strictly decreasing function on an interval.

Prove that the function f(x)=logsinx is strictly increasing in (0,pi/2) and strictly decreasing in (pi/2,pi)

Prove that the function f given by f(x) = log sin x is strictly increasing on (0,pi/(2)) and strictly decreasing on (pi/(2),pi) .

Prove that the function f given by f(x)=logsinx is strictly increasing on (0,pi/2) and strictly decreasing on (pi/2,pi)

Prove that the function log sin x is strictly increasing (0,pi/2) and strictly decreasing on (pi/2,pi)

A function f is said to be increasing/strictly increasing/decreasing/strictly decreasing at x_0, if there exists an interval I containing x_0, such that f is increasing /strictly increasing /decreasing /strictly decreasing, respectively, in I. Which of the following statements regarding the above definition is FALSE?

Show that the function f(x)=x^2 is neither strictly increasing nor strictly decreasing on R .

Show that the function f(x) = x^(2) is (a) strictly increasing on [0, oo] (b) strictly decreasing on [-oo, 0] (c) neither strictly increasing nor strictly decreasing on R

show that the function f(x)=sin x is strictly increasing in (0,(pi)/(2)) strictly decreasing in ((pi)/(2),pi)

Without using the derivative,show that the function f(x)=|x| is strictly increasing in (0,oo) strictly decreasing in (-oo,0)