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Absolute vs. Relative Maxima and Minima

  1. Jul 28, 2010 #1
    1. The problem statement, all variables and given/known data

    I do not have a specific homework problem, but could someone please clarify this for me?

    QUESTION: When you have an absolute maxima (or minima), how can you tell if it is ALSO a relative maxima (or minima)?

    I understand how to find absolute extrema on a closed interval, and how to find critical values of a function by setting f'(x) = 0 and when f'(x) is undefined.


    Thank you!
    Tina
     
    Last edited by a moderator: Jul 28, 2010
  2. jcsd
  3. Jul 28, 2010 #2

    Mark44

    Staff: Mentor

    The question is usually asked the other way around. IOW, If you have a relative maximum (or minimum), how can you tell if it is ALSO an absolute maximum (minimum)?

    It's generally easier to find relative maxima or minima by finding the values for which the derivative is zero or undefined and checking endpoints of the domain. From these points, it's just a matter of finding the overall largest and smallest to get the absolute maximum and minimum.
     
  4. Jul 28, 2010 #3
    Thanks for your response!
     
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