Partial Derivative

  1. Question: Let C be the trace of the paraboloid [tex]z=9-x^2-y^2[/tex] on the plane [tex]x=1[/tex]. Find parametric equations of the tangent line L to C at the point P(1,2,4).

    What I did:
    [tex]z=8-y^2, x=1[/tex]
    [tex]f_{y}=-2y[/tex]
    [tex]f_{y}(1,2)=-4[/tex]

    So the parametric equations of L are:
    [tex]
    x=1
    [/tex]
    [tex]
    y=2+t
    [/tex]
    [tex]
    z=4-4t
    [/tex]

    Am I doing this correct? Thanks.
     
    Last edited: Mar 11, 2006
  2. jcsd
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