So here's basically what I was taught. The Lagrangian (L) is the difference between the kinetic and potential energy:

[tex]L=K.E-P.E[/tex]

The action (denoted S) is denoted:

[tex]\int\limits_{t_1}^{t_0}L\, dt[/tex]

The problem I am having is being able to distinguish why the calculus of variations must be used rather than simple maxima and minima from calculus 1.

So, here's the point of what I need: can somebody explain to me the following things:

1. Why normal maxima and minima cannot solve this type of problem.

2. What exactly is the calculus of variations and how does it solve this type of problem.