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Math Help - [SOLVED] tangent line to the graph

  1. #1
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    Unhappy [SOLVED] tangent line to the graph

    Hey... i have no idea how to work with the y's in the equation. '
    The question is:
    Determine the equation of the tangent line to the graph of the relation with equation xy^2+x^2y=12 at the point where x=3.

    Please any help would be greatly appreciated... thanks
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  2. #2
    Eater of Worlds
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    When it's difficult to solve for y, then we can use implicit differentiation.

    xy^{2}+x^{2}y=12

    2xy\frac{dy}{dx}+y^{2}+x^{2}\frac{dy}{dx}+2xy=0

    Solve for dy/dx:

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

    Now, find the slope at x=3
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  3. #3
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    most excellent.. took me a while to understand what was going on but i got it now... however, i don't get how to find the slope!!! I can't isolate the y...
    and i have to find where x=3...

    if i try to plug it into the original equation - can't isolate y
    when i try the derivative - still can't isolate y

    how do i go about isolating the y because i get what to do afterwards it's this y that is not making sence to me!!!

    thanks
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  4. #4
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    Nevermind

    my friend cam by and i've seen the error in my ways...

    thanks
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