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Math Help - Equation of a tangent line

  1. #1
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    Equation of a tangent line

    Okay I know I am doing something wrong but I can't see my mistake - please help me

    "Find the equation of the tangent line to the curve
    3x^2 - 3y^3+2yx^2=-45 at point (-2,3)

    So first my goal is to find the derivative fox x so here I go....

    6x - 9y^2 (dy/dx) + 4xy + 2x^2(dy/dx) = 0

    dy/dx (-9y^2 + 2x^2) = -6x -4xy

    dy/dx = (-6x-4xy)/(-9y^2 + 2x^2)

    So if I plug in the point coordinates (-2,3) to calculate the slope I get

    (12 - (-24))/(-81+8) which is -36/73 so I know I am wrong b/c that just can't be the slope.

    Where am I going wrong????

    And jumping ahead ....the equation of the tangent will be
    y-3 = (slope from above) (x- -2) and then solve for y if this is wrong let me know this too - thanks

    Thanks in advance from

    this confused calculus beginner
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  2. #2
    Senior Member mollymcf2009's Avatar
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    Quote Originally Posted by calcbeg View Post
    Okay I know I am doing something wrong but I can't see my mistake - please help me

    "Find the equation of the tangent line to the curve
    3x^2 - 3y^3+2yx^2=-45 at point (-2,3)

    So first my goal is to find the derivative fox x so here I go....

    6x - 9y^2 (dy/dx) + 4xy + 2x^2(dy/dx) = 0 **Forgot a dy in middle term

    dy/dx (-9y^2 + 2x^2) = -6x -4xy

    dy/dx = (-6x-4xy)/(-9y^2 + 2x^2)

    So if I plug in the point coordinates (-2,3) to calculate the slope I get

    (12 - (-24))/(-81+8) which is -36/73 so I know I am wrong b/c that just can't be the slope.

    Where am I going wrong????

    And jumping ahead ....the equation of the tangent will be
    y-3 = (slope from above) (x- -2) and then solve for y if this is wrong let me know this too - thanks

    Thanks in advance from

    this confused calculus beginner
    You forgot your \frac{dy}{dx} on your middle term (*in red) See if that helps
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  3. #3
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    I thought that b/c I wasn't calculating the derivative of y at that moment in time that I shouldn't put a dy/dx but I guess that implies one should go in wherever there is an x or y derivative being calculated??

    Still a little confused but I will rework it this way and see what I get.

    Thanks
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