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Homework Help: What's a Saddle Point?

  1. Jan 12, 2012 #1
    I'm working through a partial differentiation problem, to which I have the answer.

    The function being 4x^2+4xy-y^3-2x+2 to which the stationary points must be obtained and classified.

    At the end of the working out, when partial differentiation is conducted and a number of -32 is obtained, it states that because this is a negative number this is a "saddle point". Is this another term for a "point of inflection"?

    How can they make this claim? I thought since the number obtained is negative it would therefore be a maximum turning point.

    The second number obtained with the second partial differentiation is 32, and it states since this is a positive number this is a minimum turning point; which I understand.

    Thank you.
  2. jcsd
  3. Jan 12, 2012 #2


    Staff: Mentor

  4. Jan 12, 2012 #3


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    Just to add to the other reply. For a function of one variable a saddle point is a point of inflection, but an inflection point need not be a saddle point since the slope need not be zero.

    For a function of two variables a saddle point is a stationary point that is neither a max nor a min point. The term "inflection point" is not used for functions of two variables that I know of.
  5. Jan 13, 2012 #4
    Thanks very much for the info guys!. Much appreciated, Thank you.
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