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Math Help - implicit differentiation

  1. #1
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    implicit differentiation

    I'm having trouble with this problem. I keep thinking I'm doing it right, but when I plug it in I'm wrong. Someone please help.

    2. x^2-3xy-2y^3=-148

    I need to find the slope of the tangent line to the curve at (2,4)

    Whelp, due date passed, thanks.
    Last edited by nobodygirl; November 8th 2006 at 06:58 PM.
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  2. #2
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    Quote Originally Posted by nobodygirl View Post
    I'm having trouble with this problem. I keep thinking I'm doing it right, but when I plug it in I'm wrong. Someone please help.

    2. x^2-3xy-2y^3=-148

    I need to find the slope of the tangent line to the curve at (2,4)

    Whelp, due date passed, thanks.
    Differentiating with respect to x we have:

    <br />
\frac{d}{dx}[x^2-3xy-2y^3]=0<br />

    <br />
2x - 3\left[x \frac{dy}{dx}+y\right]-6y^2\frac{dy}{dx}=0<br />

    So collecting the terms with the derivative and rearranging gives:

    <br />
(3x+6y)\frac{dy}{dx}=2x-3y<br />

    or:

    <br />
\frac{dy}{dx}=\frac{2x-3y}{3(x+2y^2)}=\frac{2\times 2-3 \times 4}{3(2+2\times 16)}=\frac{4}{51}<br />

    RonL
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