Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Second derivative test for x^3

  1. Sep 30, 2009 #1
    Does the second derivative test fail for x3 at x=0:
    f'(x)=3x2 f''(x)=6x ,

    for x=0,
    f'(0)=0 & f''(0)=+ve ,
    so it should be a point of local maxima , but it is not!!!!!!!!!!
     
  2. jcsd
  3. Sep 30, 2009 #2

    jbunniii

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    f''(0) is most certainly NOT positive!
     
  4. Oct 1, 2009 #3

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Since f''(0) = 0 (not +ve, whatever that means), yes, the second derivative test fails. But that doesn't mean you can't determine the type of critical point by other means.
     
  5. Oct 1, 2009 #4
    ^i
    It didn't really fail, it just hints at the possibility of an inflection point.
     
  6. Oct 1, 2009 #5

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    No, it doesn't hint at that any more than it hints at a max or min. You could have max, min, or inflection point when the first two derivatives are zero.

    And it does fail as a test distinguishing max/min.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Second derivative test for x^3
Loading...