Question

A laconic least action question.

Answer 1

S, action always 'tries' to be at a minimum.
\[\S=\int\limits_{}^{}(T-V)dt\]
,so:
\[\int\limits_{}^{}dS=\int\limits_{}^{}(T-V)dt\]
\[\int\limits_{}^{}(dS/dt)dt=\int\limits_{}^{}(T-V)dt\]
so
\[dS/dt=T-V\]

where S is always at a minimum.

1.)Is the mathematics correct so far?
2.) So this means T is always at a minimum, V at a maximum, yes?