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Math Help - Extrema test for any dimension

  1. #1
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    Extrema test for any dimension

    Given,
    f:\mathbb{R}^n\to \mathbb{R}
    countinous on a ball, has a critical point on \bold{x} is there a way to determine whether or not this point is a relative extrema?

    I am asking this because, there is a foolproof method for single variables called first-derivative test. But for two variables the second-partials test is not foolproof. I wish to know if there is one that is for two and more variables?
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  2. #2
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    there is some sort of way to check it
    i think it was with minors of the jacobian of the function

    (learned it over a year ago and almost flanked on that course)
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