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Math Help - Find the equation of the tangent line?

  1. #1
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    Find the equation of the tangent line?



    Find the equation of the tangent line to the graph of the function at z=3
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  2. #2
    MHF Contributor Unknown008's Avatar
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    Find the derivative of the function using the quotient rule:

    f(x) = \dfrac{6z^2}{5z^2 + 2z}

    f'(z) = \dfrac{(5z^2 + 2z)(12z) - (6z^2)(10z + 2)}{(5z^2 + 2z)^2}

    Put z = 3.

    f'(3) = \dfrac{(5(3)^2 + 2(3))(12(3)) - (6(3)^2)(10(3) + 2)}{(5(3)^2 + 2(3))^2}

    Simplify, then find the value of f(z) when z = 3.

    Then use:

    y = mx+ c

    m is f'(3), and c is a constant.

    To find c, use y = f(3) and x = z

    You'll get your equation of the line now. You can replace y and x by f(z) and z respectively.
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  3. #3
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    WOW. I did that and it kept turning out wrong. Turns out I used an x instead of z.
    I'm really smart.
    Thank you =)
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  4. #4
    MHF Contributor Unknown008's Avatar
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    You're welcome
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