Results 1 to 4 of 4

Math Help - Local Maxima, Minima and Points of inflections

  1. #1
    Junior Member
    Joined
    Oct 2010
    Posts
    63

    Local Maxima, Minima and Points of inflections

    So far this is what i got:
    Original eq:
    f(x)=(x+5)/(x^2-16)

    By using quotient rule i got:

    f'(x)=0=x^2-16-2x^2-10x
    0=(x+8)(x+2)
    x=-8, x=-2

    Now subbing them back into f(x) i got max and min as (correct me if im wrong):
    (-8,3/80) and (-2, -3/20)

    Point of inflection:

    f''(x)=2(x^3+15x^2+48x+80)/(x^2-16)^3

    the second derivative is right im pretty sure i just took out 2 as common factor:

    Now this is where im confused do i make the whole thing equal 0, or the top line? and how can i simplify it afterwards?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,513
    Thanks
    1404

    Re: Local Maxima, Minima and Points of inflections

    By the quotient rule, your derivative should be \displaystyle \frac{x^2 - 16 - 2x^2 - 10x}{\left( x^2 - 16 \right) ^2}. The evaluation of the x values of critical points is correct though. Note that f(-8) = -3/48 = -1/16 and f(-2) = -3/12 = -1/4. How did you determine which is a local max and which is a local min?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Oct 2010
    Posts
    63

    Re: Local Maxima, Minima and Points of inflections

    i factorised the top line and subbed -2 and -8 into f(x)
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,513
    Thanks
    1404

    Re: Local Maxima, Minima and Points of inflections

    Well you made some mistakes that I already pointed out. And what you did is not enough to show if it's a local maximum or minimum. I suggest you look up the second derivative test.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: March 28th 2011, 07:14 PM
  2. Replies: 9
    Last Post: August 2nd 2010, 02:30 PM
  3. Local Maxima and Minima
    Posted in the Calculus Forum
    Replies: 0
    Last Post: November 12th 2009, 10:04 AM
  4. local maxima and minima
    Posted in the Calculus Forum
    Replies: 6
    Last Post: October 18th 2009, 05:50 PM
  5. Local Maxima or Minima
    Posted in the Calculus Forum
    Replies: 3
    Last Post: August 10th 2009, 09:07 AM

Search Tags


/mathhelpforum @mathhelpforum