# Monotonic Functions

Monotonic functions are functions that tend to move in only one direction as x increases. A monotonic increasing function always increases as x increases, i.e. f(a)>f(b) for all a>b. A monotonic decreasing function always decreases as x increases, i.e. f(a)<f(b) for all a>b. In calculus speak, a monotonic decreasing function's derivative is always negative. A monotonic increasing function's derivative is always positive. The same sort of restrictions are also made for the monotonic non-decreasing and monotonic non-increasing functions, only the rules governing the derivative's domain are not strict inequalities. Besides lines, some monotonic functions are the exponential ex, and some polynomials where one monotonic factor outwieghs the others, like f(x) = sin(x)+4x. Because it is uncommon to find functions which strictly increase or strictly decrease, we sometimes call a function monotonic on a restricted domain. For instance, cos(x) is monotonic decreasing within 0<x<
-David