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Intermediate Value Theorem Converse

  1. Jun 23, 2016 #1
    1. The problem statement, all variables and given/known data
    I was given the problem of determining if the Converse of the Intermediate Value Theorem in my book was true. Below is my theorem from the book.

    2. Relevant equations


    3. The attempt at a solution
    I had looked at the converse and tried to draw some examples, and I am thinking it is false. I am leaning that way, because technically the function may or may not be continuous. I just need to know if I am on the right direction.
     

    Attached Files:

  2. jcsd
  3. Jun 23, 2016 #2

    Ray Vickson

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    What, exactly, would be the converse of the intermediate-value theorem?
     
  4. Jun 23, 2016 #3
    If there is at least one number c in [a,b] such that f(c)=k, then f is continuous on the closed interval [a,b] and k is any number between f(a) and f(b). I got the answer though I think.
     
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