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 Point: Stationary 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 ...

... 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 ...

... 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**...

... 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)