If takes in a (local) extremvalue and can be differentiated in , then
Fermat showed this in the 17th century.
If takes in an extremevalue and can be differentiated in then
PROOF: Look at
If is local maximum: for alla in a surrounding (close).
This about is such an important quality that it has its own name:
is called a STATIONARY POINT TO , if can be differentiated in and
A STATIONARY POINT that is NOT an extremepoint is called a SADELPUNKT.
Example) has a SADELPUNKT (terasspunkt) in