proof of Fermat’s Theorem (stationary points)
Since the limit of this ratio as exists and is equal to we conclude that . On the other hand for we notice that
but again the limit as exists and is equal to so we also have .
Hence we conclude that .
To prove the second part of the statement (when is equal to or ), just notice that in such points we have only one of the two estimates written above.
|Title||proof of Fermat’s Theorem (stationary points)|
|Date of creation||2013-03-22 13:45:09|
|Last modified on||2013-03-22 13:45:09|
|Last modified by||paolini (1187)|