TITLE: Is it possible to use physics or other form of non-canonical reasoning to study functions?
QUESTION [13 upvotes]: It is well-known (see, for example, the books New Horizons in geometry, Maxima and minima without calculus and The Mathematical Mechanic) that it is possible to use some forms of "physical reasoning", "geometric reasoning", or "probabilistic reasoning" or otherwise non-canonical arguments to find minima and maxima of some functions or to solve some problems that normally require calculus.

Are there such methods to calculate limits, find derivatives, or
  verify the continuity of a function? Could you provide some examples?

REPLY [4 votes]: Soap films create a surface with minimal surface area naturally. There is some more at this site. Here is a video. Note that these are local rather than global minima.