Stationary Point

In mathematics, particularly in calculus, a stationary point is an input to a function where the derivative is zero (equivalently, the slope is zero): where the function "stops" increasing or decreasing (hence the name).

For the graph of a one-dimensional function, this corresponds to a point on the graph where the tangent is parallel to the x-axis. For the graph of a two-dimensional function, this corresponds to a point on the graph where the tangent plane is parallel to the xy plane.

The term is mostly used in two dimensions, which this article discusses: stationary points in higher dimensions are usually referred to as critical points; see there for higher dimensional discussion.

Read more about Stationary PointStationary Points, Critical Points and Turning Points, Classification, Curve Sketching

Other articles related to "stationary point, point, stationary, points":

Stationary Point - Curve Sketching - Example
... Even though f''(x) = 0, this point is not a point of inflexion ... But, x2 is not a stationary point, rather it is a point of inflexion ... Here, x3 is both a stationary point and a point of inflexion ...
General Point Process Theory - Stationarity
... A point process is said to be stationary if has the same distribution as for all For a stationary point process, the mean measure for some constant and where stands for the Lebesgue ... This is called the intensity of the point process ... A stationary point process on has almost surely either 0 or an infinite number of points in total ...
Saddle Point - Mathematical Discussion
... A simple criterion for checking if a given stationary point of a real-valued function F(x,y) of two real variables is a saddle point is to compute the function's Hessian matrix at that point ... For example, the Hessian matrix of the function at the stationary point is the matrix which is indefinite ... Therefore, this point is a saddle point ...
Jacobian Matrix And Determinant - Jacobian Matrix - Uses - Dynamical Systems
... If F(x0) = 0, then x0 is a stationary point (also called a critical point, not to be confused with a fixed point) ... The behavior of the system near a stationary point is related to the eigenvalues of JF(x0), the Jacobian of F at the stationary point ... real part with a magnitude less than 1, then the system is stable in the operating point, if any eigenvalue has a real part with a magnitude greater than 1, then the point is unstable ...

Famous quotes containing the words point and/or stationary:

    The whole point about the true unconscious is that it is all the time moving forward, beyond the range of its own fixed laws or habits. It is no good trying to superimpose an ideal nature upon the unconscious.
    —D.H. (David Herbert)

    It is the dissenter, the theorist, the aspirant, who is quitting this ancient domain to embark on seas of adventure, who engages our interest. Omitting then for the present all notice of the stationary class, we shall find that the movement party divides itself into two classes, the actors, and the students.
    Ralph Waldo Emerson (1803–1882)