Results 1 to 3 of 3

Math Help - equation of tangent line

  1. #1
    Junior Member shepherdm1270's Avatar
    Joined
    Mar 2008
    Posts
    47

    equation of tangent line

    Find the equation of the tangent line at the given value (in form Ax+By+C=0) Implicit Differentiation must be used:

    If you could show me the steps, as well, that would be great... yet again, i'm totally lost.

    a) x^2 y^3 = 8 ; (-1,2)

    b) y^3 + xy - y = 8x^4 ; x = 1



    thanks again, guys :-/
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,550
    Thanks
    542
    Hello, shepherdm1270!

    Here's the first one . . .


    Find the equation of the tangent line at the given value
    (in the form Ax+By+C\:=\:0).
    Implicit Differentiation must be used:

    a)\;\;x^2y^3 \:=\:8\qquad(\text{-}1,2)

    Differentiate: . x^2\!\cdot\!3y^2y' + 2x\!\cdot\!y^3 \:=\:0\quad\Rightarrow\quad y' \:=\:-\frac{2y}{3x}

    At (\text{-}1,2)\!:\;\;y' \:=\:-\frac{2(2)}{3(\text{-}1)} \:=\:\frac{4}{3}\quad\hdots The slope of the tangent is \frac{4}{3}


    The line through (\text{-}1,2) with slope \frac{4}{3} is:

    . .  y - 2 \;=\;\frac{4}{3}[x - (\text{-}1)]\quad\Rightarrow\quad y - 2 \:=\:\frac{4}{3}x + \frac{4}{3}


    Multiply through by 3\!:\;\;3y - 6 \:=\:4x + 4\quad\Rightarrow\quad \boxed{ 4x - 3y + 10 \:=\:0}

    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Feb 2008
    Posts
    40
    Quote Originally Posted by shepherdm1270 View Post
    b) y^3 + xy - y = 8x^4 ; x = 1
    First of all if you sub x = 1 you'll get
    y^3=8, which means y=2

    and if we differentiate:
    y^3 + xy - y = 8x^4

    3y^2\frac{dy}{dx} + x\frac{dy}{dx} + y - \frac{dy}{dx} = 32x^3

    \frac{dy}{dx}(3y^2 + x - 1) = 32x^3 - y

    \frac{dy}{dx} = \frac{32x^3 - y}{3y^2 + x -1}

    sub x=1 and y=2 you'll get \frac{dy}{dx} = \frac{5}{2}

    y-2 =\frac{5}{2}(x-1)

    2y-4=5x-5

    5x-2y-1=0
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 6
    Last Post: January 12th 2011, 02:38 PM
  2. equation of tangent line
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: April 28th 2010, 04:16 AM
  3. equation of the tangent line
    Posted in the Calculus Forum
    Replies: 4
    Last Post: October 15th 2009, 03:14 PM
  4. tangent line equation
    Posted in the Calculus Forum
    Replies: 2
    Last Post: October 3rd 2008, 02:39 PM
  5. Equation of tangent line.
    Posted in the Calculus Forum
    Replies: 2
    Last Post: April 3rd 2008, 08:17 AM

Search Tags


/mathhelpforum @mathhelpforum