# 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 ?
The optional hands-free, adjustable stand provides flexible mounting capabilities, increasing operator comfort and efficiency for all types of merchandise.
We also plan to demonstrate the value of our solution for increasing operator productivity, tracking and analyzing power usage and predicting maintenance schedules.
The technical and safety information in the catalog will help abrasive users to lower abrasive costs while increasing operator safety and plant productivity.
Cattini concludes, "With an explosion in the use of mobile technology delivering both voice and text messages, location-based services are becoming essential customer services and therefore critical to attracting and retaining customers and increasing operator profitability.
Evana solution will improve part reliability and cycle time, while increasing operator efficiency and ergonomics
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 is very ideal in increasing operator confidence and productivity especially in jobs that require operating around other machines or workers.
0 will enable the quick roll out of plans that would create a differentiated subscriber experience while increasing operator ARPU.
Consisting of a new torque converter with Lock Up and free wheel stator, Optishift is a new system that integrates the Volvo patented Reverse-by-Braking (RBB) function--significantly reducing fuel consumption by up to 15 percent as well as increasing operator comfort and driveline durability.
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.

Site: Follow: Share:
Open / Close