In this Khan Academy video series Khan goes through the derivation of the formula for the linear regression line for some data points.
The only part I do not understand is the one I've given a link to. Particularly, I don't understand why Khan is so sure that when he sets the partial derivatives to zero, he is going to get the squared error function at its minimum (as opposed to its maximum).
How does he know that? He doesn't explain this in the video, so I believe it must be more or less obvious.
A short answer explaining this in simple terms would be much appreciated.