nonincreasing function - Wolfram|Alpha

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Input interpretation

nonincreasing function (calculus result)

Alternate names

decreasing function | monotonically decreasing function

Definition

Let f(x) be a real-valued function and let I be an interval. If f(x_1)>=f(x_2) for all x_1<x_2 in I, then f(x) is nonincreasing on the interval I. If f(x) is nonincreasing over its entire domain, then f(x) is a nonincreasing function.
It should be noted that while some authors use the term "decreasing function" to mean "nonincreasing function, " the former term is also commonly used to mean "strictly decreasing function."

Details

Concepts involved

domain of a function | function | interval

Related concepts

critical number | first derivative test | monotonic function | nondecreasing function | strictly increasing function | strictly decreasing function

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