intermediate value theorem

intermediate value theorem
a statement that claims that for each value between the least upper bound and greatest lower bound of the image of a continuous function there is a corresponding point in its domain that the function maps to that value.

Wikipedia foundation.

Игры ⚽ Нужно решить контрольную?

Look at other dictionaries:

  • 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

  • intermediate-value theorem — /in teuhr mee dee it val yooh/, Math. the theorem that a function continuous between two points and having unequal values, a and b, at the two points takes on all values between a and b. * * * …   Universalium

  • intermediate-value theorem — /in teuhr mee dee it val yooh/, Math. the theorem that a function continuous between two points and having unequal values, a and b, at the two points takes on all values between a and b …   Useful english dictionary

  • 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

  • Marginal value theorem — The optimal time spent in a patch is given by the tangent to the resource intake curve that departs from the expected transit time value. Any other line crossing the resource intake curve has a shallower slope and thus a sub optimal resource… …   Wikipedia

  • Darboux's theorem (analysis) — Darboux s theorem is a theorem in real analysis, named after Jean Gaston Darboux. It states that all functions that result from the differentiation of other functions have the intermediate value property: the image of an interval is also an… …   Wikipedia

  • Fundamental theorem of calculus — The fundamental theorem of calculus specifies the relationship between the two central operations of calculus, differentiation and integration.The first part of the theorem, sometimes called the first fundamental theorem of calculus, shows that… …   Wikipedia

  • Rolle's theorem — In calculus, a branch of mathematics, Rolle s theorem essentially states that a differentiable function, which attains equal values at two points, must have a stationary point somewhere between them.tandard version of the theoremIf a real valued… …   Wikipedia

  • Brouwer's fixed point theorem — ▪ topology       in mathematics, a theorem of algebraic topology (topology) that was stated and proved in 1912 by the Dutch mathematician L.E.J. Brouwer (Brouwer, Luitzen Egbertus Jan). Inspired by earlier work of the French mathematician Henri… …   Universalium

  • Complex conjugate root theorem — In mathematics, the complex conjugate root theorem states that if P is a polynomial in one variable with real coefficients, and a + bi is a root of P with a and b real numbers, then its complex conjugate a − bi is also a root… …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”