Results 1 to 3 of 3

Math Help - Calc problem find the curve.

  1. #1
    Newbie
    Joined
    Nov 2006
    Posts
    3

    Exclamation Calc problem find the curve.

    for the certain curve, (d2*y) / (dx2) = 18x-8

    If the slope of the line tangent to the curve is 9 at the point (1, -1), find the equation of the curve.

    Thanks a lot!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by mightymax View Post
    for the certain curve, (dˆ2*y) / (dxˆ2) = 18x-8

    If the slope of the line tangent to the curve is 9 at the point (1, -1), find the equation of the curve.

    Thanks a lot!

    We see (dˆ2*y) / (dxˆ2) = 18x-8, this just means the second derivative of some function y is 18x-8, so here goes.

    (dˆ2*y) / (dxˆ2) = 18x-8
    => dy/dx = 9x^2 - 8x + C ..................integrated both sides to reverse the derivative
    dy/dx gives equation for the slope, which is 9 when x = 1
    => 9 = 9(1)^2 - 8(1) + C
    => C = 8

    So dy/dx = 9x^2 + 8x + 8
    => y = 3x^3 - 4x^2 + 8x + D .................again integrated both sides
    we have the point (1,-1), so y=-1, when x = 1
    => -1 = 3(1)^3 - 4(1)^2 + 8(1) + D
    => D = -8

    So the curve is y = 3x^3 - 4x^2 + 8x - 8
    Last edited by Jhevon; March 1st 2007 at 04:54 AM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,829
    Thanks
    123
    Quote Originally Posted by mightymax View Post
    for the certain curve, (d2*y) / (dx2) = 18x-8

    If the slope of the line tangent to the curve is 9 at the point (1, -1), find the equation of the curve.

    Thanks a lot!
    Hi,

    if y = f(x) then

    f'(x) = ∫(18x-8) dx = 9x-8x+C

    You know that f'(1) = 9. Therefore

    f'(1) = 9 - 8 + C = 9 ===> C = 8 and f'(x) = 9x - 8x + 8

    f(x) = ∫(9x - 8x + 8)dx = 3x - 4x + 8x + C

    You know that f(1) = -1 . Therefore

    f(1) = 3 - 4 + 8 + C = -1 ===> C = -8

    The term of the function is:

    f(x) = 3x - 4x + 8x -8

    EB
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: September 21st 2011, 07:21 PM
  2. Replies: 1
    Last Post: February 24th 2010, 06:17 PM
  3. Calc volume / area between curve help:
    Posted in the Calculus Forum
    Replies: 7
    Last Post: January 11th 2010, 05:55 AM
  4. Replies: 8
    Last Post: October 13th 2009, 05:04 PM
  5. Calc 1 area of plane curve
    Posted in the Calculus Forum
    Replies: 2
    Last Post: December 7th 2008, 11:59 AM

Search Tags


/mathhelpforum @mathhelpforum