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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?

    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


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    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

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    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


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    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.
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