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Math Help - Third-Order Partial Derivatives

  1. #1
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    Third-Order Partial Derivatives

    Hi. For a two-variable function, at point Z all first-partials are zero, all second-order-partials are zero, but fxxx (third-order-partial) is non-zero. Is Z is local minimum, maximum, or neither?

    I can't use the second derivative test because it's 0 which is inconclusive.

    I think it could either be a minimum or maximum. But I don't know why...
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  2. #2
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    Are you familiar with the Hessian determinant?
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