MINIMA AND MAXIMA
Max/min problems tend to be well suited for the physical approach. The reason for this is perhaps the fact many physical systems find maxima or minima automatically: a pendulum finds the minimum of potential energy; the light from a pebble on the bottom of the pool to my retina chooses the path of least time; a soap bubble chooses the shape of least volume; a chain hanging by two ends chooses the shape of lowest center of mass, and so on—the list is endless.
Here is a common pattern in finding a physical solution. Let us say we have to minimize a function. The main step is to invent a mechanical system whose potential energy is the given function. The minimum of the function corresponds to the minimum of the potential energy, ...