1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

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


    User Avatar
    Science Advisor

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