Results 1 to 6 of 6

Math Help - quick implicit differentiation question

  1. #1
    Member
    Joined
    Sep 2007
    Posts
    76

    quick implicit differentiation question

    ok just a question about the working out for this problem,

    I understand

    4x^2 - 8xy - 9y^2 = -637

    = 8x - 8y - 8x d/dx(y) - d/dy(9y^2)dy/dx

    = 8x - 8y - 8x dy/dx - 18y dy/dx

    but where does the + sign come from??? can anyone explicitly show where this comes from.. I think it must come from the product rule but I just cant see it...

    (8x-8y)-(8x+18y)dy/dx
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Aug 2007
    Posts
    239
    They just factored it.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by dankelly07 View Post
    ok just a question about the working out for this problem,

    I understand

    4x^2 - 8xy - 9y^2 = -637

    => 8x - 8y - 8x d/dx(y) - d/dy(9y^2)dy/dx = 0

    => 8x - 8y - 8x dy/dx - 18y dy/dx = 0

    but where does the + sign come from??? can anyone explicitly show where this comes from.. I think it must come from the product rule but I just cant see it...

    => (8x-8y)-(8x+18y)dy/dx = 0
    NB: I realise what you're trying to say. Nevertheless, the editing (in red) I've done is essential - otherwise what's posted makes no mathematical sense. I can assure you that if this was an answer submitted in an examination or assignment it would lose marks if given in its original form.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    Sep 2007
    Posts
    76
    ok now I'm wondering for a implicit differentiation problem, how i determine a local max, local min or if the case is degenerate? any help would be ace..
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member
    Joined
    Jun 2008
    Posts
    792
    A local minimum is a point c such that f(c) \le f(x) for all x in an open interval containing c.
    A local maximum is a point c such that f(c) \ge f(x) for all x in an open interval containing c.

    Best points to focus on is the critical points, the points where the derivative of the function does not exist or equals 0. Plug these critical points in the original function.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Member
    Joined
    Sep 2007
    Posts
    76
    <br />
\frac{{dy}}<br />
{{dx}} = \frac{{8x - 8y}}<br />
{{8x + 18y}} = 0<br />

    <br />
\begin{gathered}<br />
  8x - 8y = 0 \hfill \\<br />
   =  > x = y \hfill \\ <br />
\end{gathered} <br />

    <br />
\begin{gathered}<br />
  4x^2  - 8x^2  - 9x^2  =  - 637 \hfill \\<br />
   - 13x^2  =  - 637 =  > x^2  = 49 \hfill \\<br />
  x =  \pm 7 \hfill \\<br />
  ( - 7, - 7)and(7,7) \hfill \\ <br />
\end{gathered} <br />


    so are these the 'critical points'? is the first point a local min and the second a local max?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Quick implicit differentiation question
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 3rd 2011, 02:49 AM
  2. Implicit Differentiation question
    Posted in the Calculus Forum
    Replies: 11
    Last Post: February 12th 2010, 02:18 AM
  3. Replies: 2
    Last Post: November 14th 2009, 05:11 PM
  4. Quick Implicit Differentiation
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 17th 2008, 09:46 PM
  5. Quick Question on Implicit Differentiation
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 28th 2008, 06:21 PM

Search Tags


/mathhelpforum @mathhelpforum