Results 1 to 3 of 3

Math Help - d2y/dx2 at point (-2,1)

  1. #1
    Member
    Joined
    Sep 2009
    Posts
    124

    Post d2y/dx2 at point (-2,1)

    Find d2y/dx2 at point (-2,1) for y^2-2x-4y-1=0

    so i tired moving the xs and constants over:
    y^2-4y=2x+1
    but then I'm stuck...
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor chisigma's Avatar
    Joined
    Mar 2009
    From
    near Piacenza (Italy)
    Posts
    2,162
    Thanks
    5
    The explicit expression for y(x) is found resolving the algebraic equation...

    y^{2} - 4 y - 2x -1 =0 (1)

    ... and we obtain...

    y = 2 \pm \sqrt {2x+5} (2)

    Because is y(-2) =1 we have to choose in (2) the sign '-', so that is...

    \frac{d^{2} y}{dx^{2}} = (2x+5)^{- \frac{3}{2}} = 1 _{x=-2} (3)

    Kind regards

    \chi \sigma
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    14,973
    Thanks
    1121
    You don't need to solve for y, use "implicit differentiation".

    Since y^2- 4y- 2x- 1= 0, 2yy'- 4y'- 2= 0. Set y= 1 and solve for y'.

    Do it again: 2y'(y')- 2yy''- 4y''= 2(y')^2- 2yy''- 4y''= 0. Set y= 1, and y' equal to the value you just found, and solve for y''.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 6
    Last Post: May 16th 2011, 04:57 AM
  2. Replies: 1
    Last Post: April 6th 2011, 06:44 AM
  3. Singular point: How can I numerically find the point of fracture?
    Posted in the Advanced Applied Math Forum
    Replies: 5
    Last Post: January 4th 2011, 02:30 AM
  4. Replies: 9
    Last Post: July 20th 2010, 08:00 AM
  5. Replies: 3
    Last Post: February 20th 2008, 10:17 AM

Search Tags


/mathhelpforum @mathhelpforum