The point at which a very significant change occurs; a decisive moment.
A turning point is a discrimen, one of the two marked points on a cursus or classical-period race-track.
The concept of the discrimen is used figuratively in describing events such as those of the fortune of war, which, having tended in one direction, then tend in the opposite way. A turning point is thus a crisis.
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The stationary points in this graph are all relative maxima or relative minima.
In mathematics, particularly in calculus, a stationary point is a point on the graph of a function where the tangent to the graph is parallel to the x-axis (in 2D) or the plane tangent to the surface is parallel to the XY plane (in 3D).
A point of inflection is not necessarily a stationary point.