Aside from Extreme Value Theorem (EVT), there is another theorem behind optimization, the Fermat’s Theorem: Let f be a continuous function on an open interval I where c is in I. If f has an extremum...

Aside from Extreme Value Theorem (EVT), there is another theorem behind optimization, the Fermat’s Theorem:

Let
f
be a continuous function on an open interval I where
c
is in I. If
f
has an extremum at
c, then
c
must be a critical number of
f.

Expound this theorem.