Results 1 to 3 of 3

Math Help - find # of points where a curve has a horizontal tangent line

  1. #1
    Newbie
    Joined
    Dec 2008
    Posts
    4

    find # of points where a curve has a horizontal tangent line

    I am to find the number of points (by hand ) where the curve x^2 - xy + (3/4)y^2 = 7 has horizontal tangent lines.

    what i did was i took the derivative:

    2x-y+(3/2)y = 0

    simplified:

    2x - (1/2) y = 0

    solved for y:

    2x = (1/2)y
    4x = y

    plugged it into the original to find my x value

    x=+/- sqrt(7)/3

    what do i do from here?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Oct 2008
    Posts
    1,035
    Thanks
    49
    Quote Originally Posted by Synth3t1c View Post
    I am to find the number of points (by hand ) where the curve x^2 - xy + (3/4)y^2 = 7 has horizontal tangent lines.

    what i did was i took the derivative:

    2x-y+(3/2)y = 0
    Follow the chain rule for the y term, so that's (3/2)y as you say but then times dy/dx.

    Use the product rule for the xy - so that'll be x times the derivative of y (for which you'll just have to write dy/dx), plus (or minus) y times the derivative of x (which is the part you did).
    Then solve for dy/dx...
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Oct 2008
    Posts
    1,035
    Thanks
    49


    As usual, straight continuous lines differentiate (downward) with respect to x, straight dashed lines with respect to the dashed balloon expression. So the left triangular network is a 'product-rule shape' and the other one a 'chain-rule shape'.

    Don't integrate - balloontegrate! Balloon Calculus: worked examples from past papers
    Last edited by tom@ballooncalculus; December 9th 2008 at 10:01 AM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 10
    Last Post: November 21st 2009, 05:16 AM
  2. Replies: 3
    Last Post: March 28th 2009, 09:18 PM
  3. Replies: 5
    Last Post: January 11th 2009, 11:19 PM
  4. Replies: 2
    Last Post: October 26th 2008, 05:28 AM
  5. Replies: 0
    Last Post: October 24th 2007, 06:23 PM

Search Tags


/mathhelpforum @mathhelpforum