A function f(x) increases on an interval I if f(b)>=f(a) for all b>a, where a, b element I. If f(b)>f(a) for all b>a, the function is said to be strictly increasing. Conversely, a function f(x) decreases on an interval I if f(b)<=f(a) for all b>a with a, b element I. If f(b)a, the function is said to be strictly decreasing. If the derivative f'(x) of a continuous function f(x) satisfies f'(x)>0 on an open interval (a, b), then f(x) is increasing on (a, b). However, a function may increase on an interval without having a derivative defined at all points. For example, the function x^(1/3) is increasing everywhere, including the origin x = 0, despite the fact that the derivative is not defined at that point.

decreasing function | derivative | nondecreasing function | nonincreasing function | strictly decreasing function | strictly increasing function