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Unformatted text preview: 16.8.10 Defining a Saddle Point (SP) The Harper Collins Dictionary of Mathematics : A point on a surface that is a maximum in one planar crosssection and a minimum in another. Visualizing a hyperbolic paraboloid helps. The definition may vary. Are degenerate "ties" allowed along a crosssection, like for horizontal lines? Also, for example, are the points along the yaxis saddle points if we have the graph of the "snake cylinder" f x , y ( ) = x 3 ? Orientation of axes: < x y That's debatable. Using the Harper Collins definition, I don't believe they would be; the thing just doesn't look like a "saddle" along the yaxis. But it is true that there are higher and lower points "immediately around" those points. Incidentally, D = 0 everywhere for this function, so the 2 nd Derivative Test says nothing. See: http://en.wikipedia.org/wiki/Saddle_point...
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 Spring '11
 staff
 Calculus, Derivative

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