Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook