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)
“...there is a difference between being convinced and being stubborn. I’m not certain what the difference is, but I do know that if you butt your head against a stone wall long enough, at some point you realize the wall is stone and that your head is flesh and blood.”
—Maya Angelou (b. 1928)