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Local extremum at endpoints

  1. Feb 28, 2008 #1
    I thought local extremum did not exist at the endpoints of a closed bounded interval, however my textbook claims this.

    Wikipedia:

    "A continuous (real-valued) function on a compact set always takes maximum and minimum values on that set. An important example is a function whose domain is a closed (and bounded) interval of real numbers (see the graph above). The neighborhood requirement precludes a local maximum or minimum at an endpoint of an interval."
     
  2. jcsd
  3. Feb 28, 2008 #2

    Dick

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    If you consider a 'neighborhood' to be a 'neighborhood in the domain' your textbook is right. If you consider it to be a 'neighborhood in the reals' then Wikipedia is right. There are a lot of terms that are defined somewhat differently in different references. I think you'd better live by your textbooks definition. Until you change textbooks.
     
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