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 e^x, 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