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

Identifying local maximum, local minimum and saddle point.

  1. Oct 20, 2014 #1
    Indicate whether you think it is a local maximum, local minimum, saddle point, or none of these?

    615d6b88-0905-30da-8b9f-5d95379e82e4___38df22d3-72ff-3595-8d9b-53259de06ff3_zpsc9b9bd2b.png
    My solution:

    Point P = Local Max
    Point Q = Local Min
    Point R = None
    Point S = Saddle

    I got a 75% for first attempt, so one answer is not correct and I am not sure which one isn't.
     
  2. jcsd
  3. Oct 23, 2014 #2

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    The circle around Q is confusing. If it is really +1, it should have a zero ring around it. If it is -1 (what I would expect), where is the minus sign?
    Same problem with the circle to the right of R, just with reversed signs.

    Either R or Q give the issue, which one depends on those sign problems.
     
  4. Oct 27, 2014 #3

    Ben Niehoff

    User Avatar
    Science Advisor
    Gold Member

    Actually the problem with Q is bigger than that. The 0 contour is marked in the picture: it is the pair of diagonal lines going through S. Given the 1 contour around Q, where should the 0 contour go? There must be one between -1 and 1 (unless the function is discontinuous on a ring around Q, in which case the problem is evil). But if the 0 contour is a ring around Q, then what to make of the 0 contour that is already drawn going through S? Either these contours must join up (possibly at R?), or there must be an additional local min/max somewhere between Q and the origin. Either way, it seems that important information has been omitted from the plot.
     
  5. Oct 27, 2014 #4

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    This cannot be the whole 0 contour for a continuous function. There is a path from a -1 to a +1 contour which has to have a 0 somewhere.
    Where is the problem? (x^2-y^2)^2*((x-1)^2+y^2-0.1) has this type of contours.
    It does not have to, but even if it has, where is the problem?
    Certainly, as there is no 0 contour or the contour labels are wrong.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Identifying local maximum, local minimum and saddle point.
  1. Local invariants (Replies: 7)

  2. Local Maximum (Replies: 1)

Loading...