1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    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! :)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook