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
Famous quotes containing the words stationary and/or point:
“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)
“A route differs from a road not only because it is solely intended for vehicles, but also because it is merely a line that connects one point with another. A route has no meaning in itself; its meaning derives entirely from the two points that it connects. A road is a tribute to space. Every stretch of road has meaning in itself and invites us to stop. A route is the triumphant devaluation of space, which thanks to it has been reduced to a mere obstacle to human movement and a waste of time.”
—Milan Kundera (b. 1929)