Results 1 to 5 of 5

Math Help - algebra minus

  1. #1
    Junior Member
    Joined
    Sep 2012
    From
    sthlm
    Posts
    53

    algebra minus

    Find f''\left( x \right)=0 when f\left( x \right)=\frac{\left( x-1 \right)^{2}}{1+x^{2}}

    Attempt: https://dl.dropbox.com/u/586465/2012...2016.48.57.jpg

    the thing is: I get +3 instead of -3.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,527
    Thanks
    773

    Re: algebra minus

    The derivative is correct. -2x^2+x^2+3 = 3 - x^2.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Mar 2011
    From
    Tejas
    Posts
    3,367
    Thanks
    735

    Re: algebra minus

    first derivative:

    f'(x) = \frac{(1+x^2)(2(x-1)) - (x-1)^2(2x)}{(1+x^2)^2}

    = \frac{2x^3 - 2x^2 + 2x - 2 - (2x^3 - 4x^2 + 2x)}{(1+x^2)^2}

    = \frac{2x^2 - 2}{(1+x^2)^2}.

    second derivative:

    f''(x) = \frac{(1+x^2)^2(4x) - (2x^2 - 2)(2(1+x^2)(2x))}{(1+x^2)^4}

    = \frac{(1+x^2)(4x) - (2x^2 - 2)(4x)}{(1+x^2)^3}

    = \frac{4x^3 + 4x - 8x^3 + 8x}{(1+x^2)^3}

     = \frac{(4x)(3 - x^2)}{(1+x^2)^3}.

    now if f''(x) = 0, the numerator must be 0, so:

    (4x)(3-x^2) = 0.

    thus either 4x = 0, and x = 0, or: 3-x2 = 0, in which case:

    x = \pm \sqrt{3}

    (your error was in taking -2x2 + x2 to be x2, instead of -x2).
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Sep 2012
    From
    sthlm
    Posts
    53

    Re: algebra minus

    the last line, "your error was in taking -2x2 + x2 to be x2, instead of -x2", would've sufficed, but gee… Thank you so much!
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor

    Joined
    Mar 2011
    From
    Tejas
    Posts
    3,367
    Thanks
    735

    Re: algebra minus

    perhaps so, but future readers of this thread may not click on, or view the image link you posted.

    also, i'm no computational prodigy, but a bit more like a turtle: slow and sure wins the race. so to keep things straight in my mind, i have to verify. every. single. step (i discovered several computational errors before i finished my post). derivatives involving quotients are particularly nasty, because of the many opportunities for sign errors involved.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Difference between plus minus and minus plus
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: December 23rd 2011, 04:14 AM
  2. Minus on denominator again
    Posted in the Algebra Forum
    Replies: 7
    Last Post: October 12th 2009, 07:37 AM
  3. plus/minus in TeX
    Posted in the LaTeX Help Forum
    Replies: 2
    Last Post: May 7th 2009, 03:44 PM
  4. phi(x/2) and w(x) minus pi(x)=???
    Posted in the Number Theory Forum
    Replies: 0
    Last Post: April 7th 2009, 03:30 AM
  5. Minus problems
    Posted in the Algebra Forum
    Replies: 2
    Last Post: November 6th 2008, 11:42 AM

Search Tags


/mathhelpforum @mathhelpforum