Increasing and Decreasing Functions definition of Increasing and Decreasing Functions in the Free Online Encyclopedia.

Functions, Increasing and Decreasing

A function y = f(x) is called increasing over an interval [a, b] if for any pair of points x and*’, a ≤ x ≤ the inequality f(x)≤f(x’) is satisfied and strictly increasing if the inequality f(x)< f(x’) is satisfied. Decreasing and strictly decreasing functions are similarly defined. For example, the function y = x2 (Figure 1, a) strictly increases over the interval [0, 1], and y = l/(x 1) (Figure 1, b) strictly decreases over this interval. Increasing functions are designated as f(x)1 and decreasing functions a.sf(x) I. In order for a differentiable function f(x) to be increasing over an interval [a, b], it is necessary and sufficient that its derivative f’(x) be nonnegative over [a, b].

Figure 1

In addition to the increase and decrease of a function over an interval, the increase and decrease of a function at a point are considered. The function y =f(x) is called increasing at a point Jt0 if an interval (α, β) can be found containing point x₀ such that for any point x from (α, β), x > x₀, the inequality f(x₀) f(x) is satisfied and that for any point jc from (α, β), x ≤ x₀, the inequality f(x) f(x) ≤ f(x₀) is satisfied. The strict increase of a function at point x₀ is similarly defined. If f(x0) > 0, then the function/fjcj strictly increases at point x0. lff(x) increases at every point of the interval (a, b), then it increases over this interval.

REFERENCE

Fikhtengol’ts, G. M. Kurs differentsial’nogo i integral’nogo ischisleniia, 6th ed., vol. 1. Moscow, 1966.

S. B. STECHKIN

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No references found	Derivatives of implicit functions, derivatives up to order two, geometrical interpretation of the derivative, tangents and normal, increasing and decreasing functions, maximum and minimum values of a function, Roll's Theorem and Lagrange's Mean Value Theorem. Math's Syllabus for IIT JEE by Vanya Tiwari / Science and technology, general community	Incompleteness incompressibility incompressibility condition incompressible flow incompressible fluid Inconel Inconfidencia Week incongruous inconnu inconsistent inconsistent axioms inconsistent equations inconsistent inequalities incontinence incontinent incorporate Incorporated Macmillan Incorporating Languages Incorporation incorporeal Incorrect DOS version incorrigible incrassate Increased Productivity of Labor, Law of increaser Increasing and Decreasing Functions increasing function Increasing Requirements, Law of increasing sequence increment increment borer incremental analysis incremental backup incremental compiler incremental computer incremental constraint solver incremental cost incremental digital recorder incremental dump tape incremental frequency shift incremental hysteresis loss incremental induction incremental mode incremental permeability incremental printer Incremental Prototyping Technology for Embedded Realtime Systems incremental representation Incretion incross Incrustation Incrustation Style	Increased urine production Increased urine production Increased urine production increased value Increased Violence Changes the Debate Increased Violence Changes the Debate Increased Violence Changes the Debate Increased Violence Changes the Debate Increased water consumption Increased water consumption Increased water consumption Increased-Take-Home-Pay Increased/Improved Performance Engine Increaseful Increasement Increasement increaser increaser increaser increaser increases increases increases Increases exponentially Increases exponentially increasing increasing increasing increasing Increasing Absolute Risk Aversion Increasing and Decreasing Functions Increasing Capacity to Meet Demand Increasing Degrees of Contraction Increasing Failure Rate Increasing Failure Rate Average Increasing function Increasing function Increasing Generalized Failure Rate Increasing Leadership Effectiveness Increasing Mean Residual Life Increasing Minority Awareness of Genetics Now increasing monotonic Increasing operator Increasing opportunity cost Increasing opportunity cost Increasing Premium Whole Life Increasing Radius Search Increasing Relative Risk Aversion Increasing Requirements, Law of Increasing returns to scale Increasing sequence Increasing sequence Increasing sequence Increasing sequence Increasing Term Rider Increasing Vocational Learning Opportunities for Indigenous Students increasingly increasingly increasingly increate increately

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Derivatives of implicit functions, derivatives up to order two, geometrical interpretation of the derivative, tangents and normal, increasing and decreasing functions, maximum and minimum values of a function, Roll's Theorem and Lagrange's Mean Value Theorem.

Math's Syllabus for IIT JEE by Vanya Tiwari / Science and technology, general community

Incompleteness

incompressibility

incompressibility condition