What is the difference between a point of inflection and a saddle point?
What is the difference between an extremum and a stationary point?
2026-02-23 02:11:09.1771812669
Saddle point, point of inflection, extremum, stationary point
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A point of inflexion is a point where the tangent line exists and crosses the curve. So the context is the graph of a 1-dimensional curve in 2 dimensions. A saddle point is a point on a surface (so the context is a two dimensional surface in 3 dimensions.) where the tangent plane is horizontal, but the point is neither a max or a min.
A stationary point is a point where the derivative exists and is zero. It may or may not be an extremum. An extremum is either a local max or local min. For instance the function $f(x) = |x|$ has a local min at $x=0$, but the derivative doesn't exist, and therefore it is not a stationary point.