Stationary Point and Stationary Curve

A stationary point is a point at which the differential of a function vanishes. A stationary curve is a curve at which the variation of a function vanishes.

For a function of one variable y = f(x), the tangent to the graph of the function at a stationary point is parallel to the x-axis. The plane tangent to the surface z = f(x, y) at a stationary point of the function of two variables f(x, y) is parallel to the xy-plane.