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 "point, stationary, stationary point, points":

... 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 ...

... 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 ...

... 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 ... 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**...

### Famous quotes containing the words point and/or stationary:

“The trouble with Reason is that it becomes meaningless at the exact *point* where it refuses to act.”

—Bernard Devoto (1897–1955)

“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)