Fermat’s theorem (stationary points)

Let f:(a,b) be a continuous functionMathworldPlanetmathPlanetmath and suppose that x0(a,b) is a local extremum of f. If f is differentiableMathworldPlanetmathPlanetmath in x0 then f(x0)=0.

Moreover if f has a local maximumMathworldPlanetmath at a and f is differentiable at a (the right derivative exists) then f(a)0; if f has a local minimum at a then f(a)0. If f is differentiable in b and has a local maximum at b then f(b)0 while if it has a local minimum at b then f(b)0.

Title Fermat’s theorem (stationary points)
Canonical name FermatsTheoremstationaryPoints
Date of creation 2013-03-22 13:45:05
Last modified on 2013-03-22 13:45:05
Owner paolini (1187)
Last modified by paolini (1187)
Numerical id 7
Author paolini (1187)
Entry type Theorem
Classification msc 26A06
Related topic ProofOfLeastAndReatestValueOfFunction
Related topic LeastAndGreatestValueOfFunction