Minimum Distance from a Point to a Curve (Calculus)

In this video we use calculus to find the minimum distance between a curve and point (in this case the origin (0,0)).  We sketch, write a distance function, square the distance, take a derivative, prove we're getting a minimum, and then write our solution.  This is a common optimization problem.

This is definitely a AP Calculus AB, Calc BC, and Calc 1 topic that you'll see along the way.