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Extreme Value Theorem true for constants?

  1. Aug 28, 2014 #1
    My textbook says the extreme value theorem is true for constants but I don't buy it. I mean I suppose that every value over a closed interval for a constant would be a maximum and a minimum technically but it seems like BS to me. Can anyone explain why this BS is true?
     
  2. jcsd
  3. Aug 29, 2014 #2
    Constant functions are continuous, I don't really understand what your issue is. Can you elaborate about why this is bs?
     
  4. Aug 29, 2014 #3
    No, my problem is the extreme value theorem says that for a continuous function on a closed interval there will be a minimum and maximum value. My complaint with that is for a constant every point is a minimum and a maximum and I just think that is pretty lame so I'm mad.
     
  5. Aug 29, 2014 #4
    Well, okay then.
     
  6. Aug 29, 2014 #5
    Well thanks for your answer, my problem isn't with my understanding of it I just don't really like it. However, your point about the theorem saying that the function must simply have a min and max makes sense, I suppose that the min and max don't have to be different and not be at every point; I still don't like it though.
     
  7. Aug 29, 2014 #6
    As a follow up question, how would you define the maximum and minimum of a function? Do you know the definition or do you just find it is not pleasing to how one thinks about maximum and minimum?
     
  8. Aug 29, 2014 #7
    Max= highest value the function reaches
    Min= lowest value a function reaches

    So for a constant yes they would have both technically. Like I said I just think it's poop.
     
  9. Aug 29, 2014 #8
    But I do see what you're saying and I appreciate your logic. Thank you.
     
  10. Aug 29, 2014 #9
    Hmm, Alright.
     
  11. Aug 29, 2014 #10
    Did you get my message?
     
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