Increasing - Decreasing Functions - Definitions

Strictly increasing functions

A function f(x) is said to be a strictly increasing function on (a,b) if

x1 is less than x2 => f(x1) is l.t.f(x2) for all x1,x2 Є (a,b)

Strictly decreasing functions

A function f(x) is said to be a strictly increasing function on (a,b) if

x1 l.t. x2 => f(x1)g.t.f(x2) for all x1,x2 Є (a,b)

Monotonic function

A function f(x) is said to be monotonic on (a,b) if it is either increasing or decreasing on the interval (a,b)

Increasing or decreasing on [a,b]

A function f(x) is said to be an increasing (decreasing) function on [a,b] if it is increasing (decreasing) on (a,b) and it also increasing (decreasing) at x =a and x =b.

Increasing or decreasing at a point

A function f(x) is said to be a increasing (decreasing) at a point x0 if there is an interval (x0-h, x0+h) containing x0 such that f(x) is increasing (decreasing) on (x0-h, x0+h).