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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. In algebraic geometry an inflection point is defined slightly more generally, as a 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. ==Equivalent forms== A differentiable function has an inflection point at (''x'', ''f''(''x'')) if and only if its first derivative, ''f′'', has an isolated extremum at ''x''. (This is not the same as saying that ''f'' has an extremum). That is, in some neighborhood, ''x'' is the one and only point at which ''f′'' has a (local) minimum or maximum. If all extrema of ''f′'' are isolated, then an inflection point is a point on the graph of ''f'' at which the tangent crosses the curve. For an algebraic curve, a non singular point is an inflection point if and only if the multiplicity of the intersection of the tangent line and the curve (at the point of tangency) is odd and greater than 2.〔http://www.encyclopediaofmath.org/index.php/Point_of_inflection〕 For a curve given by parametric equations, a point is an inflection point if its signed curvature changes from plus to minus or from minus to plus, i.e., changes sign.〔http://mathworld.wolfram.com/InflectionPoint.html〕 For a twice differentiable function, an inflection point is a point on the graph at which the second derivative changes sign. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「inflection point」の詳細全文を読む スポンサード リンク
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