# Fermat theorem

From Encyclopedia of Mathematics

A necessary condition for a local extremum of a real-valued function. Suppose that a real-valued function is defined in a neighbourhood of a point and is differentiable at that point. If has a local extremum at , then its derivative at is equal to zero: . Geometrically this means that the tangent to the graph of at the point is horizontal. A condition equivalent to this for extrema of polynomials was first obtained by P. Fermat in 1629, but it was not published until 1679.

#### Comments

For Fermat's theorems in number theory see Fermat great theorem; Fermat little theorem.

**How to Cite This Entry:**

Fermat theorem.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Fermat_theorem&oldid=18337

This article was adapted from an original article by L.D. Kudryavtsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article