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单词 Minimum point
释义

Minimum point

原声例句
可汗学院:统计学(视频版)

The slope at that point in that direction will also be 0, and that is our minimum point.

该点在该方向的斜率也将为 0,这就是我们的最小点。

可汗学院:统计学(视频版)

Because at this minimum point, I guess you could say in three dimensions, this minimum point on the surface is going to occur when the slope with respect to m and the slope with respect to b is 0.

因为在这个最小点, 我想你可以说在三维空间中,当相对于 m 的斜率和相对于 b 的斜率是 0 时, 表面上的这个最小点就会出现。

中文百科

驻点 Stationary point

(重定向自Minimum point)
y = x + sin(2x) 的图像
驻点(红色)与拐点(蓝色),这图像的驻点都是局部极大值或局部极小值。
y = x3 的图像  原点(0,0)是驻点,但不是局部极值。

在微积分,驻点Stationary Point)又称为临界点Critical Point)或平稳点,即函数在该点的一阶导数为零,也就是说若 p 为临界点/驻点则

在这一点,函数的输出值停止增加或减少。

对于一维函数的图像,驻点的切线平行于x轴。对于二维函数的图像,驻点的切平面平行于xy平面。

值得注意的是,一个函数的驻点不一定是这个函数的极值点(考虑到这一点左右一阶导数符号不改变的情况);反过来,在某设置区域内,一个函数的极值点也不一定是这个函数的驻点(考虑到边界条件)。

英语百科

Stationary point 驻点

(重定向自Minimum point)
The stationary points are the red circles. In this graph, they are all relative maxima or relative minima. The blue squares are inflection points.
A graph in which local extrema and global extrema have been labeled.
Saddle points (stationary points that are neither local maxima nor minima: they are inflection points. The left is a
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).
Not to be confused with a fixed point where x = f(x).

In mathematics, particularly in calculus, a stationary point or critical point of a differentiable function of one variable is a point of the domain of the function where the derivative is zero (equivalently, the slope of the graph at that point is zero). Informally, it is a point where the function "stops" increasing or decreasing (hence the name).

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更新时间:2025/6/17 22:33:38