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- Critical_point_(mathematics) abstract "In mathematics, a critical point or stationary point of a differentiable function of a real or complex variable is any value in its domain where its derivative is 0. For a differentiable function of several real variables, a critical point is a value in its domain where all partial derivatives are zero. The value of the function at a critical point is a critical value.The interest of this notion lies in the fact that the point where the function has a local extremum are critical points.This definition extends to differentiable maps between Rm and Rn, a critical point being, in this case, a point where the rank of the Jacobian matrix is not maximal. It extends further to differentiable maps between differentiable manifolds, as the points where the rank of the Jacobian matrix decreases. In this case, critical points are also called bifurcation points.In particular, if C is a plane curve, defined by an implicit equation f(x,y) = 0, the critical points of the projection onto the x-axis, parallel to the y-axis are the points where the tangent to C are parallel to the y-axis, that is the points where In other words, the critical points are those where the implicit function theorem does not apply.The notion of critical point allows to explain an astronomical phenomenon that was mysterious before Copernicus. A stationary point in the orbit of a planet is a point of the trajectory of the planet on the celestial sphere, where the motion of the planet seems to stop before restarting in the other direction. This occurs because of a critical point of the projection of the orbit into the ecliptic circle.".
- Critical_point_(mathematics) thumbnail Stationary_vs_inflection_pts.svg?width=300.
- Critical_point_(mathematics) wikiPageID "1951424".
- Critical_point_(mathematics) wikiPageRevisionID "600892908".
- Critical_point_(mathematics) hasPhotoCollection Critical_point_(mathematics).
- Critical_point_(mathematics) subject Category:Multivariable_calculus.
- Critical_point_(mathematics) subject Category:Singularity_theory.
- Critical_point_(mathematics) subject Category:Smooth_functions.
- Critical_point_(mathematics) type Abstraction100002137.
- Critical_point_(mathematics) type Function113783816.
- Critical_point_(mathematics) type MathematicalRelation113783581.
- Critical_point_(mathematics) type Relation100031921.
- Critical_point_(mathematics) type SmoothFunctions.
- Critical_point_(mathematics) comment "In mathematics, a critical point or stationary point of a differentiable function of a real or complex variable is any value in its domain where its derivative is 0. For a differentiable function of several real variables, a critical point is a value in its domain where all partial derivatives are zero.".
- Critical_point_(mathematics) label "Critical point (mathematics)".
- Critical_point_(mathematics) label "Kritisch punt (wiskunde)".
- Critical_point_(mathematics) label "Kritischer Punkt (Mathematik)".
- Critical_point_(mathematics) label "Point critique (mathématiques)".
- Critical_point_(mathematics) label "Ponto crítico (funções)".
- Critical_point_(mathematics) label "Punkt krytyczny (matematyka)".
- Critical_point_(mathematics) label "Punto critico (matematica)".
- Critical_point_(mathematics) label "Punto crítico (matemáticas)".
- Critical_point_(mathematics) label "Критическая точка (математика)".
- Critical_point_(mathematics) label "نقطة حرجة (رياضيات)".
- Critical_point_(mathematics) sameAs Kritischer_Punkt_(Mathematik).
- Critical_point_(mathematics) sameAs Punto_crítico_(matemáticas).
- Critical_point_(mathematics) sameAs Point_critique_(mathématiques).
- Critical_point_(mathematics) sameAs Punto_critico_(matematica).
- Critical_point_(mathematics) sameAs 임계점_(수학).
- Critical_point_(mathematics) sameAs Kritisch_punt_(wiskunde).
- Critical_point_(mathematics) sameAs Punkt_krytyczny_(matematyka).
- Critical_point_(mathematics) sameAs Ponto_crítico_(funções).
- Critical_point_(mathematics) sameAs m.068fg_.
- Critical_point_(mathematics) sameAs Q577705.
- Critical_point_(mathematics) sameAs Q577705.
- Critical_point_(mathematics) sameAs Critical_point_(mathematics).
- Critical_point_(mathematics) wasDerivedFrom Critical_point_(mathematics)?oldid=600892908.
- Critical_point_(mathematics) depiction Stationary_vs_inflection_pts.svg.
- Critical_point_(mathematics) isPrimaryTopicOf Critical_point_(mathematics).
