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Summary

An inflection point is a point on a curve at which the sign of the curvature changes.
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It is defined as a regular point where the tangent meets the curve to order at least 3
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, and an undulation point or hyperflex is defined as a point where the tangent meets the curve to order at least 4.
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Inflection points may be stationary points, but are not local maxima or local minima.
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They can be found by considering where the second derivative changes signs.
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Summaries from the best pages on the web

Summary
In algebraic geometry an inflection point is defined slightly more generally, as a regular point where the tangent meets the curve to order at least 3, and an undulation point or hyperflex is defined as a point where the tangent meets the curve to order at least 4.

Inflection point - Wikipedia
wikipedia.org

Summary
An inflection point is a point on a curve at which the sign of the curvature (i.e., the concavity) changes. Inflection points may be stationary points , but are not local maxima or local minima . For example, for the curve plotted above, the point is an inflection point.

Inflection Point -- from Wolfram MathWorld
wolfram.com

Summary
Inflection points are points where the function changes concavity, i.e. from being "concave up" to being "concave down" or vice versa. They can be found by considering where the second derivative changes signs.

Inflection points introduction (video) | Khan Academy
khanacademy.org

An Inflection Point is where a curve changes from Concave upward to Concave downward (or vice versa)

Inflection Points
mathsisfun.com

Definition of an Inflection Point {{x_0},{x_0} + \delta } \right)\), and is convex downward on the other, then \({x_0}\) is called a point of inflection of the ...

Inflection Points
math24.net