# 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.

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

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 measure ... 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 ...
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 ... 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 ...
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 ...