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Math Help - Need help with implicit differentiation!

  1. #1
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    Need help with implicit differentiation!

    Well, it's not so much the differentiating I need help with. we have this (2x-x^2y^2=4y-4) formula, and need to use implicit differentiation to find the leftmost point of the graph. figured out that dy/dx = (1-xy^2)/(2-x^2y), guessing I need solve it equal to 0.

    Tried solving dy/dx = 0, got y=+/- sqrt(x-1) and tried substituting it into the original formula but that was incorrect. I'm stuck!
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  2. #2
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    Re: Need help with implicit differentiation!

    dy/dx = 0? Why would that help you find a VERTICAL asymptote? Try dx/dy.
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  3. #3
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    Re: Need help with implicit differentiation!

    Quote Originally Posted by TKHunny View Post
    dy/dx = 0? Why would that help you find a VERTICAL asymptote? Try dx/dy.
    Well you might aswell find dy/dx, and see where its not defined since dx/dy is the reciprocal of dy/dx
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  4. #4
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    Re: Need help with implicit differentiation!

    What's the difference? Anyway, one should also be sure of two other things, besides dx/dy = 0:

    1) dy/dx is not also zero, and
    2) dx/dy doesn't have some other value as well as zero.

    We are looking for a left-most point.
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  5. #5
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    Re: Need help with implicit differentiation!

    \frac{dy}{dx}=0\Rightarrow y=\pm \sqrt{\frac{1}{x}}
    not  \pm \sqrt{x-1} !!!!!!!!
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