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Math Help - Vector Tangent Line Problem

  1. #1
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    Vector Tangent Line Problem

    1. The problem statement, all variables and given/known data

    Let f(x,y) = 5y^(2)-(2x^(2)+xy)

    Then an implicit equation for the tangent plane to the graph of f at the point (0,-2) is




    3. The attempt at a solution
    I understand that I should take the derivative to find the gradient vector. For the derivative, I get <-4x-y,10y-x>.

    I plug in (O,-2) and get <2,-20>.

    My question is, what should I do to put this into implicit form??

    Thanks!
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  2. #2
    MHF Contributor

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    Yes, you should take the gradient vector but you are taking the gradient of the wrong function. You want to take the gradient of the function F(x,y,z)= z- f(x,y)= z- 5y^2+ 2x^2+ xy= 0. The gradient of a function is always perpendicular to a "level curve" of the function.
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