# mean value theorem

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mean value theorem
a statement that claims that given an arc of a differentiable curve, there is at least one point on that arc at which the derivative of the curve is equal to the average derivative of the arc.

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• Mean value theorem — For the theorem in harmonic function theory, see Harmonic function#Mean value property. Topics in Calculus Fundamental theorem Limits of functions Continuity Mean value theorem Differential calculus  Derivative Change of variables …   Wikipedia

• mean-value theorem — ▪ mathematics       theorem in mathematical analysis dealing with a type of average useful for approximations and for establishing other theorems, such as the fundamental theorem of calculus (analysis).  The theorem states that the slope of a… …   Universalium

• mean value theorem — vidutinės vertės teorema statusas T sritis fizika atitikmenys: angl. mean value theorem vok. Mittelwertsatz, m rus. теорема о среднем значении, f pranc. théorème de la moyenne, m …   Fizikos terminų žodynas

• mean value theorem — noun 1. : a theorem in differential calculus: if a function of one variable is continuous on a closed interval and differentiable on the interval minus its endpoints there is at least one point where the derivative of the function is equal to the …   Useful english dictionary

• mean value theorem — Math. the theorem that for a function continuous on a closed interval and differentiable on the corresponding open interval, there is a point in the interval such that the difference in functional values at the endpoints is equal to the… …   Universalium

• mean value theorem — noun Date: 1900 1. a theorem in differential calculus: if a function of one variable is continuous on a closed interval and differentiable on the interval minus its endpoints there is at least one point where the derivative of the function is… …   New Collegiate Dictionary

• Mean value theorem (divided differences) — In mathematical analysis, the mean value theorem for divided differences generalizes the mean value theorem to higher derivatives.[1] It states that for any n + 1 points x0, ..., xn in the domain of an n times differentiable… …   Wikipedia

• mean-value theorems — In mathematics, two theorems, one associated with differential calculus and one with integral calculus. The first proposes that any differentiable function defined on an interval has a mean value, at which a tangent line is parallel to the line… …   Universalium

• Mean value analysis — In queueing theory, a specialty within the mathematical theory of probability, mean value analysis is a technique for computing expected queue lengths in equilibrium for a closed separable system of queues. It was developed by Reiser and… …   Wikipedia

• Intermediate value theorem — In mathematical analysis, the intermediate value theorem states that for each value between the upper and lower bounds of the image of a continuous function there is a corresponding value in its domain mapping to the original.Intermediate value… …   Wikipedia