Results 1 to 6 of 6

Math Help - Stationary Point of a parametric function.

  1. #1
    Junior Member
    Joined
    Dec 2008
    From
    London
    Posts
    45

    Stationary Point of a parametric function.

    A curve is defined by the equation x^2y+y^3 =  2x+1

    a)Find the gradient at (2,1)

    a)Workings

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

    x^2\frac{dy}{dx}+2xy+3y^2\frac{dy}{dx} = 2

     \frac{dy}{dx}(x^2+3y^2) = 2-2xy

     \frac{dy}{dx}= \frac{2-2xy}{x^2+3y^2}

     \frac{dy}{dx}= \frac{2-2(1)(2)}{(2)^2+3(1)^2}

     \frac{dy}{dx}= \frac{2-4}{4+3}

     \frac{dy}{dx}= -\frac{2}{7}

    b) Show that the x-cordinate of any stationary point of this curve satisfies the equation

    \frac{1}{x^3}=x+1

    b) Workings

    \frac{dy}{dx}=0

    \frac{2-2xy}{x^2+3y^2}=0

    now what? :S
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Calculus26's Avatar
    Joined
    Mar 2009
    From
    Florida
    Posts
    1,271
    so you have 2 - 2xy = 0

    from which y =1/x

    Plug this into the original equation:

    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Dec 2008
    From
    London
    Posts
    45
    isnt 2-2xy = 3y^2+x^2
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor Calculus26's Avatar
    Joined
    Mar 2009
    From
    Florida
    Posts
    1,271
    From



    What is 0 * (x^2 +3*y^2) ?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Dec 2008
    From
    London
    Posts
    45
    Gosh you make me feel so stupid :{
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor Calculus26's Avatar
    Joined
    Mar 2009
    From
    Florida
    Posts
    1,271
    We all have our moments -- I've spent hours on pblms because of simple mistakes

    Don't forget your interpretation of the problem and mechanics were excellent.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Stationary point...
    Posted in the Calculus Forum
    Replies: 7
    Last Post: June 9th 2010, 06:57 PM
  2. stationary point
    Posted in the Calculus Forum
    Replies: 1
    Last Post: August 2nd 2009, 09:24 PM
  3. stationary point
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: November 16th 2008, 01:45 AM
  4. stationary point of multivariable function
    Posted in the Calculus Forum
    Replies: 4
    Last Post: April 21st 2008, 09:04 AM
  5. stationary point
    Posted in the Calculus Forum
    Replies: 3
    Last Post: May 10th 2006, 11:38 AM

Search Tags


/mathhelpforum @mathhelpforum