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Homework Help: Exception to second derivative test? (Or am I doing something wrong?)

  1. May 14, 2012 #1
    1. The problem statement, all variables and given/known data
    I'd always used the 2nd derivative test for the nature of stationary points. But I came across this equation in one of my exercises, for which the test doesn't seem to work at all.

    Find the stationary points of: y=(x^2-1)4, stating the nature of each.

    2. Relevant equations
    Using normal calc: the stationary points are at (-1,0), (0,1) and (1,0)

    3. The attempt at a solution
    Although the double derivative works for when x=0, (local max)

    When I sub in the values x=1 or x=-1, the value I end up with is 0: suggesting that these points are stationary points of inflection, when they are not (they're actually local minima).

    Please help. :)
     
  2. jcsd
  3. May 14, 2012 #2

    tiny-tim

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    Science Advisor
    Homework Helper

    Hi Dramacon! :smile:

    From http://en.wikipedia.org/wiki/Inflection_point#A_necessary_but_not_sufficient_condition :wink:

    A necessary but not sufficient condition

    If x is an inflection point for f then the second derivative, f″(x), is equal to zero if it exists, but this condition does not provide a sufficient definition of a point of inflection. One also needs the lowest-order (above the second) non-zero derivative to be of odd order (third, fifth, etc.). If the lowest-order non-zero derivative is of even order, the point is not a point of inflection. (An example of such a function is y = x4).​
     
  4. May 14, 2012 #3
    Ah, I see! Thank you! :)
     
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