Results 1 to 3 of 3

Math Help - What did I do wrong on this implicit differentiation problem

  1. #1
    Junior Member
    Joined
    Oct 2013
    From
    United States
    Posts
    39

    What did I do wrong on this implicit differentiation problem

    Im supposed to find the slope of the tangent line at the point (3,2) for the function (4x^2+2y^2)^2-4x^2y=1864
    So here's what I did
    2(4x^2+2y^2)(8x+4yy')-4(2xy+x^2y')=0
    (8x^2+4y^2)(8x+4yy')-8xy-4x^2y'=0
    64x^3+32x^2yy'+32y^2x+16y^3y'-8xy-4x^2y'=0

    y'(32x^y+16y^3-4x^2)=-64x^3-32y^2x+8xy

    y'=(-64x^3-32y^2x+8xy)/(32x^2y+16y^3-4x^2)

    So I plugged in the x and y values to get the slope but webwork says its incorrect, I thought I smacked the bullseye dead center but apparently I messed up somewhere... if anyone can take a look and see what mistakes I made I would appreciate it! Thank You!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,804
    Thanks
    115

    Re: What did I do wrong on this implicit differentiation problem

    Quote Originally Posted by rhcprule3 View Post
    Im supposed to find the slope of the tangent line at the point (3,2) for the function (4x^2+2y^2)^2-4x^2y=1864
    So here's what I did
    2(4x^2+2y^2)(8x+4yy')-4(2xy+x^2y')=0
    (8x^2+4y^2)(8x+4yy')-8xy-4x^2y'=0
    64x^3+32x^2yy'+32y^2x+16y^3y'-8xy-4x^2y'=0

    y'(32x^y+16y^3-4x^2)=-64x^3-32y^2x+8xy

    y'=(-64x^3-32y^2x+8xy)/(32x^2y+16y^3-4x^2)

    So I plugged in the x and y values to get the slope but webwork says its incorrect, I thought I smacked the bullseye dead center but apparently I messed up somewhere... if anyone can take a look and see what mistakes I made I would appreciate it! Thank You!
    Hello,

    all your calculations are OK.

    Unfortunately you didn't mention which result you've got. I got y'=-\frac{512}{167}

    With the coordinates of the tangent point and this slope the equation of the tangent is

    y = -\frac{512}{167}  \cdot x + \frac{1882}{167}

    For confirmation I've attached a sketch of the ellipse and it's tangent.
    Attached Thumbnails Attached Thumbnails What did I do wrong on this implicit differentiation problem-tangentanellips.png  
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Oct 2013
    From
    United States
    Posts
    39

    Re: What did I do wrong on this implicit differentiation problem

    strange, i got -3.089 and i typed your answer in but its still incorrect.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: October 17th 2012, 08:01 AM
  2. Implicit differentiation problem (I think?)
    Posted in the Calculus Forum
    Replies: 2
    Last Post: January 9th 2011, 06:21 PM
  3. Implicit Differentiation Problem
    Posted in the Calculus Forum
    Replies: 2
    Last Post: February 12th 2010, 10:46 AM
  4. Replies: 0
    Last Post: February 15th 2008, 08:10 PM
  5. Implicit Differentiation Problem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 9th 2007, 12:50 PM

Search Tags


/mathhelpforum @mathhelpforum