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词汇 Inflexion point
分类 英语词汇 英语翻译词典
释义

Inflexion point

中文百科

拐点 Inflection point

（重定向自Inflexion point）
y=x3的函数图形，原点是其拐点
反正切函数的拐点
Gráfico de y = x3 con un punto de inflexión en el punto (0,0).
Gráfico de y = x3, rotado, con tangente en el punto de inflexión en el punto (0,0).

拐点（Inflection point）或反曲点是一条可微曲线改变凹凸性的点，或者等价地说，是使切线穿越曲线的点。

决定曲线的拐点有助于理解曲线的外形，这在描绘曲线图形时特别有用。

英语百科

Inflection point 拐点

（重定向自Inflexion point）
Plot of y = x³ with inflection point of (0,0), also a saddle point.
The roots, turning points, stationary points, inflection point and concavity of a cubic polynomial x³ - 3x² - 144x + 432 (black line) and its first and second derivatives (red and blue).
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.
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