Inflection point

Plot of f(x) = sin(2x) from −π/4 to 5π/4; note f’s second derivative is f″(x) = –4sin(2x). Tangent is blue where the curve is convex (above its own tangent), green where concave (below its tangent), and red at inflection points: 0, π/2 and π

y = x4 – x has a 2nd derivative of zero at point (0,0), but it is not an inflection point because the fourth derivative is the first higher order non-zero derivative (the third derivative is zero as well).

In differential calculus, an inflection point, point of inflection, flex, or inflection (inflexion) is a point on a curve at which the curve changes from being concave (concave downward) to convex (concave upward), or vice versa.

A point where the curvature vanishes but does not change sign is sometimes called a point of undulation or undulation point.

单词	Undulation point
释义	Undulation point 英语百科 Inflection point In differential calculus, an inflection point, point of inflection, flex, or inflection (inflexion) is a point on a curve at which the curve changes from being concave (concave downward) to convex (concave upward), or vice versa. A point where the curvature vanishes but does not change sign is sometimes called a point of undulation or undulation point.
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Undulation point

Inflection point