Results 1 to 2 of 2

Thread: a question about inflection points

  1. #1
    Junior Member
    Oct 2009

    a question about inflection points

    If there is a maximum and a minimum on a curve, will the inflection point between them be exactly in the middle? Or can it be located anywhere within the distance between the maximum and the minimum?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor matheagle's Avatar
    Feb 2009
    I don't think so.
    Let y=ax^3+bx^2

    Then y'=3ax^2+2bx giving maxs/mins at x=0,-2b/(3a)

    And y''=6ax+2b giving infl pts at x=-b/(3a)
    which is half way inbetween.

    Now even if we change that to y=ax^3+bx^2+cx+d
    the inflection pt is the same (x that is)
    while the max/min is the solution to 3ax^2+2bx+c=0
    which gives x={-2b\pm\sqrt{4b^2-12ac}\over 6a} and that average is once again -b/(3a)

    So it is true for polynomials of degree 3.

    Moving onto the next power...

    Try y'=x^3-3x^2+2x giving mins at x=0 and 2 and a max at 1

    while y''=3x^2-6x+2 giving infl pts at x=1\pm 1/\sqrt{3}

    and those two inflection pts are not at .5 and 1.5, the midpoints of 0 and 1, and of 1 and 2.
    Last edited by matheagle; November 20th 2009 at 11:56 PM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: August 24th 2011, 11:35 AM
  2. Replies: 5
    Last Post: April 11th 2010, 07:03 AM
  3. Inflection Points question
    Posted in the Calculus Forum
    Replies: 2
    Last Post: November 12th 2009, 11:52 AM
  4. Question about inflection points
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 28th 2009, 08:02 PM
  5. Replies: 5
    Last Post: February 27th 2009, 07:48 PM

Search Tags

/mathhelpforum @mathhelpforum