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Math Help - Finding a Tangent Line

  1. #1
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    Finding a Tangent Line

    How can I go about finding a tangent line for the following:

    (x^3)*(R^5)=1 at the point (x,R)=(1,1)

    I took the derivative of the equation but I didn't know where to go after that.
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  2. #2
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    Re: Finding a Tangent Line

    \frac{dR}{dx} is the slope of the curve at any point (x,R) on the curve ...

    evaluate the derivative at x = 1 , R = 1 to find the slope of the tangent line at that specific point, then use the point-slope form of a linear equation ...

    R - R_1 = m(x - x_1)
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  3. #3
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    Re: Finding a Tangent Line

    So if I take the derivative I get:

    3*R^5*X^2

    Then if I evaluate that at x=1, R=1 I get:

    3*1^5*1^2 = 3

    So the point slope of the linear equation should be the following:

    R - 1 = 3 ( X - 1)
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  4. #4
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    Re: Finding a Tangent Line

    That is not the derivative. Since R is a function of x, you will need to use implicit differentiation.
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  5. #5
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    Re: Finding a Tangent Line

    x^3 \cdot R^5 = 1

    solve for R in terms of x ...

    R = x^{-\frac{3}{5}}

    ... now find \frac{dR}{dx}
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  6. #6
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    Re: Finding a Tangent Line

    so the derivative would actually be:

    dr/dx = -3/(5*x^(8/5))
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    Re: Finding a Tangent Line

    ok ... find the equation of the tangent line.
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  8. #8
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    Re: Finding a Tangent Line

    so the equation should be:

    R - 1 = -3/5(x-1)
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