[brrrrrm]

> When using least squares, a zero derivative always marks a minimum. But that's not true in general ... To tell the difference between a minimum and a maximum, you'd need to look at the second derivative.

It's interesting to continue the analysis into higher dimensions, which have interesting stationary points that require looking at the matrix properties of a specific type of second order derivative (the Hessian) https://en.wikipedia.org/wiki/Saddle_point

In general it's super powerful to convert data problems like linear regression into geometric considerations.