当在最小值点的时候，两个梯度向量就垂直了。

When I am at a minimum, the two gradient vectors are parallel.

youdao

接着，我们找最小值点，会发现它不是临界点。

But then, when we are looking for the minimum of a function, well, it is not at a critical point.

youdao

也就是说，如果你可以解出来或者去除掉这些变量的点，就是临界点，当你有这样的问题要解决的时候，我们找到临界点了，它们一定是最大值点或者最小值点吗？

That means if you were able to solve and eliminate the variable that would be a critical point. When you have the same problem, as we have critical points, are they maxima or minima?

youdao

And so, I need to cheat a little bit on the drawing and make sure that this minimum occurs right here.

所以，我需要在画时作点弊,以确保最小值出现在这儿。

麻省理工公开课 - 固态化学导论课程节选