Results 1 to 11 of 11

Math Help - end-point extrema

  1. #1
    Senior Member
    Joined
    Oct 2009
    Posts
    447

    end-point extrema

    Is this book wrong about point B? I think it is an end-point but not an end-point minimum. The function at 0 has a lower value.
    Attached Thumbnails Attached Thumbnails end-point extrema-end-point-extrema.jpg  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Oct 2011
    Posts
    5

    Re: end-point extrema

    Book is correct here:
    And end-point minimum if there exists a region in the domain for which B is an end-point (you agreed it's true) and for which f(B)\leq x, \forall x . Note: if exists a region, so it doesn't have to be for every region (that would be definition of minimum), but only for a region (in this example use [3,4])
    Last edited by magicka; October 7th 2011 at 04:18 AM. Reason: Mistake
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member
    Joined
    Oct 2009
    Posts
    447

    Re: end-point extrema

    Thanks. I had started to think it is correct. Surely you are talking about B not A?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Oct 2011
    Posts
    5

    Re: end-point extrema

    yes, my mistake, I've edited previous post!
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Senior Member
    Joined
    Oct 2009
    Posts
    447

    Re: end-point extrema

    In this example C and D are end-point minimums aren't they?
    Attached Thumbnails Attached Thumbnails end-point extrema-end-point-minimums.jpg  
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Oct 2011
    Posts
    5

    Re: end-point extrema

    Nope; even though they satisfy second condition they are not endpoints!
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Senior Member
    Joined
    Oct 2009
    Posts
    447

    Re: end-point extrema

    They are end-points of the second and third functions. The book definitely describes these as end-points.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Newbie
    Joined
    Oct 2011
    Posts
    5

    Re: end-point extrema

    Could you please copy here how end-point is exactly defined?

    And you are watching endpoints of f(x), not every part of it. By that logic you could split function above (one that is defined on -2 to 4) split into infinite many parts and have infinite many end-points.
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Senior Member
    Joined
    Oct 2009
    Posts
    447

    Re: end-point extrema

    Unfortunately it is not defined.
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Senior Member
    Joined
    Oct 2009
    Posts
    447

    Re: end-point extrema

    The book does talk about C and D as being at end-points of the subdomains.
    Follow Math Help Forum on Facebook and Google+

  11. #11
    Senior Member
    Joined
    Oct 2009
    Posts
    447

    Re: end-point extrema

    This is a good guide to piecewise functions and extrema: Powered by Google Docs
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 6
    Last Post: May 16th 2011, 04:57 AM
  2. Replies: 9
    Last Post: July 20th 2010, 08:00 AM
  3. Absolute Extrema, Local Extrema
    Posted in the Calculus Forum
    Replies: 2
    Last Post: November 23rd 2009, 03:08 AM
  4. Replies: 1
    Last Post: November 18th 2009, 11:22 PM
  5. Replies: 3
    Last Post: February 20th 2008, 10:17 AM

Search Tags


/mathhelpforum @mathhelpforum