Saddle Point -- from Wolfram MathWorld

A point of a function or surface which is a stationary point but not an extremum. An example of a one-dimensional function with a saddle point is f(x)=x^3, ... Algebra AppliedMathematics CalculusandAnalysis DiscreteMathematics FoundationsofMathematics Geometry HistoryandTerminology NumberTheory ProbabilityandStatistics RecreationalMathematics Topology AlphabeticalIndex NewinMathWorld CalculusandAnalysis Calculus MaximaandMinima SaddlePoint Apointofafunctionorsurfacewhichisastationary pointbutnotanextremum.Anexampleofaone-dimensional functionwithasaddlepointis,which has (1) (2) (3) Thisfunctionhasasaddlepointatbytheextremumtestsinceand . Surfacescanalsohavesaddlepoints,whichthesecondderivativetestcansometimesbeusedtoidentify.Examplesofsurfaces withasaddlepointincludethehandkerchief surfaceandmonkeysaddle. SeealsoGameSaddlePoint,Hyperbolic FixedPoint,SecondDerivativeTest ExplorewithWolfram|Alpha Morethingstotry: saddlepoint betonevensinsingle0roulette d^4/dt^4(Ai(t)) Citethisas: Weisstein,EricW."SaddlePoint."From MathWorld--AWolframWebResource.https://mathworld.wolfram.com/SaddlePoint.html Subjectclassifications CalculusandAnalysis Calculus MaximaandMinima Created,developedandnurturedbyEricWeissteinatWolframResearch