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Math Help - Implicit Differentiation Help

  1. #1
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    Implicit Differentiation Help

    I am dumbfounded on what I am doing wrong with this problem. I was given the following problems.

    Find the equation of the tangent line to the curve (a hyperbola)
    at the point . The equation of this tangent line can be written in the form where
    m=
    b=

    I am not sure what to do. Please help! Sorry for the spam of threads tonight got a exam tomorrow.
    Last edited by jwebb19; October 3rd 2007 at 09:49 PM.
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    Bump!
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  3. #3
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    Quote Originally Posted by jwebb19 View Post
    I am dumbfounded on what I am doing wrong with this problem. I was given the following problems.






    Find the equation of the tangent line to the curve (a hyperbola)





    at the point . The equation of this tangent line can be written in the form where
    m=
    b=

    I am not sure what to do. Please help! Sorry for the spam of threads tonight got a exam tomorrow.
    the slope is equal to:

    <br />
m=\frac{dy}{dx}<br />

    Now we differentiate the equation for the curve with respect to x:

    <br />
\frac{d}{dx} \left[ \frac{x^2}{16} - \frac{y^2}{4} \right]=0<br />

    <br />
\frac{2 x}{16} - \frac{2 y}{4} \frac{dy}{dx} =0<br />

    so:

    <br />
\frac{dy}{dx}=\frac{x}{4y}<br />

    Now plug in the values of x and y to find dy/dx which gives you your m.

    Finaly plug the values of m,\ x, and y into the equation for the line abd find b

    RonL
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