Vector Calculus 21: Torricelli's Problem, a Vector-Analytic Solution

[michaelten-pow]

Thanks for producing these videos. They are so helpful in building an intuition to aid in self-study. I think that "little n sub b" and "little n sub c" are switched. Is that right?

[douglas]

Is there a way to proof why we are at the minimum and not the maximum point of the function when the derivative is zero? I know that it’s easy to see geometrically in this example, because the further we move away from the point towards infinity, the bigger the sum becomes.
But for other line shapes it may not be so obvious (like a concentric spiral that starts near the point and ends at the point for an example).