proof of least and greatest value of function
is continuous, so it will transform compact sets into compact sets. Thus since is compact, is also compact. will thus attain on the interval a maximum and a minimum value because real compact sets are closed and bounded.
Consider the maximum and later use the same argument for to consider the minimum.
If the maximum isn’t attained in and since it must be attained in either or is a maximum.
For the minimum consider and note that will verify all conditions of the theorem and that a maximum of corresponds to a minimum of and that .
|Title||proof of least and greatest value of function|
|Date of creation||2013-03-22 15:52:09|
|Last modified on||2013-03-22 15:52:09|
|Last modified by||cvalente (11260)|