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Continous or not?

  1. Oct 21, 2006 #1
    Please see attached image for reference.

    Here is the problem. Determine from the graph whether the function has any absolute extreme values on [a, b]. Then explain how your answer is consistent with Theorem 1.

    So Theorem 1 is the one that states f(x) has a maximum and minimum if F(x) is continuous on a closed interval [a,b]

    If you look at the image you will see the graph. I think that this graph is not continuous. And so I said there is no maximum or minimum. but the book says maximum x = c minimum x = a. So I guess this graph is continuous according to the book. but how is the attached image continuous in the interval [a,b]
     

    Attached Files:

  2. jcsd
  3. Oct 21, 2006 #2

    Hurkyl

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    The book never said that...
     
  4. Oct 21, 2006 #3

    HallsofIvy

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    The book says that
    "If a function, f(x) is continuous on the closed, bounded, interval [a,b] then f(x) takes on maximum and minimum values in the interval".

    It does NOT say
    "If a function takes on maximum and minimum values on [a, b] then it is continuous on the interval". That is the "converse" of the book statement and is FALSE!

    (If a statement says "if A then B", its converse is "If B then A". A statement being true does NOT mean its converse is.)
     
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