单词tangent plane
un.: 切面；切线平面
网络: 切平面；切面公差；相切平面
切线平面
切面
Say you have a minimum, well, the tangent plane at this point, at the bottom of the graph is going to be horizontal.
如果你说这是个极小值，那么这点的切平面应该是水平的。
Well, that means the gradient is actually perpendicular to the tangent plane or to the surface at this point.
那意味着，梯度向量在这点上，垂直于切平面或者是等值面。
Well, one way to think about it is in terms of tangent plane approximation.
我们可以从用切平面逼近的想法来入手。
And now what this approximation formula here says is that, in fact, the graph of a function is close to the tangent plane.
这里这个近似式的意思是，函数图象和切平面靠得很近。
If we were moving on the tangent plane, this would be an actual equality.
如果我们在切平面上移动，这将会是一个真正的等式。
That"s the equation of a tangent plane.
这就是切平面的方程。
Let"s think about the tangent plane with regard to a function f.
我们来考虑，关于函数f的一个切平面。
In fact, when we turn this into an equality, that would mean that we replace f by the tangent plane.
其实，看这个等式，就是用切平面上的值来近似f的值。
And, here"s a tangent plane at the given point.
在这个给定的点有一个切平面。
We are replacing the graph by its tangent plane.
我们用函数的切平面来替代它的图像。