# Monotonic Function

(redirected from Increasing operator)

## monotonic function

[¦män·ə¦tän·ik ′fəŋk·shən]
(mathematics)

## Monotonic Function

(or monotone function), a function whose increments Δf(x) = f(x′) − f(x) do not change sign when Δx = x′ − x > 0; that is, the increments are either always nonnegative or always nonpositive. Somewhat inaccurately, a monotonic function can be defined as a function that always varies in the same direction. Different types of monotonic functions are represented in Figure 1. For example, the function y = x3 is an increasing function. If a function f(x) has a derivative f′(x) that is nonnegative at every point and that vanishes only at a finite number of individual points, then f(x) is an increasing function. Similarly, if f′(x) ≤ 0 and vanishes only at a finite number of points, then f(x) is a decreasing function.

Figure 1

A monotonicity condition can hold either for all x or for x on a given interval. In the latter case, the function is said to be monotonic on this interval. For example, the function y = increases on the interval [−1,0] and decreases on the interval [0, +1]. A monotonic function is one of the simplest classes of functions and is continually encountered in mathematical analysis and the theory of functions. If f(x) is a monotonic function, then the following limits exist for any X0:

and

References in periodicals archive ?
For example, SME's SLT220 remote-controlled jack system can, with a single lift, elevate a complete axle of a 240- to 400-ton truck, reducing tire maintenance time and increasing operator safety.
The possible benefits for the Navy include improving operational efficiencies, increasing operator and technician safety and reducing mean time to repair.
Increasing operator comfort, the SR210 also has a large cab and one of the lowest entry threshold,
The tightly strapped insulation wrap over the ceramic coating "virtually eliminates" heat losses to the workplace, saving on air-conditioning costs and increasing operator safety.
This means that tests can be performed with both sides of the breaker grounded, increasing operator safety by eliminating the risk of high voltages being induced into the breaker under test.
This is very ideal in increasing operator confidence and productivity especially in jobs that require operating around other machines or workers.
Simple click-and-go icons help lean an operation while increasing operator productivity and order accuracy.
Innovative technical design has enhanced the cab's ergonomics, increasing operator comfort and provides all-round visibility.
The unit features a four-foot infeed magazine accommodating approximately 200 cases or blanks, thus increasing operator pro ductivity when the machine is running at its maximum speed of 60 cases per minute.
Completely air-powered, the tank can be operated where wet environmental conditions are an issue, increasing operator convenience and safety.
Oscar Mayer[R] and Louis Rich[R] cured luncheon meats are currently in the process of incorporating the new ingredient technology--a specific combination of USDA-approved ingredients, sodium and potassium lactate and sodium diacetate--further increasing operator confidence and ensuring consumer enjoyment.
Shredder operators are well aware that dust suppression benefits them in many ways, by: 1) Avoiding nuisance complaints and unhealthy emissions; 2) Increasing operator visibility; and 3) keeping metallic dust in the stream of recovered and marketable materials.

Site: Follow: Share:
Open / Close