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Concept information

mathematical analysis > real analysis > Fermat's theorem
mathematical analysis > calculus > differential calculus > Fermat's theorem

Terme préférentiel

Fermat's theorem  

Définition(s)

  • In mathematics, Fermat's theorem (also known as interior extremum theorem) is a method to find local maxima and minima of differentiable functions on open sets by showing that every local extremum of the function is a stationary point (the function's derivative is zero at that point). Fermat's theorem is a theorem in real analysis, named after Pierre de Fermat. By using Fermat's theorem, the potential extrema of a function , with derivative , are found by solving an equation in . Fermat's theorem gives only a necessary condition for extreme function values, as some stationary points are inflection points (not a maximum or minimum). The function's second derivative, if it exists, can sometimes be used to determine whether a stationary point is a maximum or minimum.
    (Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Fermat%27s_theorem_(stationary_points))

Concept(s) générique(s)

Synonyme(s)

  • interior extremum theorem

Traductions

URI

http://data.loterre.fr/ark:/67375/PSR-PTNR1PV1-4

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RDF/XML TURTLE JSON-LD Date de création 02/08/2023, dernière modif. 02/08/2023