Inflection point

Point where the curvature of a curve changes sign

In differential calculus and differential geometry, an inflection point, point of inflection, flex, or inflection (rarely inflexion) is a point on a smooth plane curve at which the curvature changes sign. In particular, in the case of the graph of a function, it is a point where the function changes from being concave (concave downward) to convex (concave upward), or vice versa. For the graph of a function f of differentiability class C2 (its first derivative f', and its second derivative f'', exist and are continuous), the condition f'' = 0 can also be used to find an inflection point since a point of f'' = 0 must be passed to change f'' from a positive value (convex) to a negative value (concave) or vice versa as f'' is continuous; an inflection point of the curve is where f'' = 0 and changes its sign at the point (from positive to negative or from negative to positive).

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