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Math Help - Equation of tangent plane

  1. #1
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    Equation of tangent plane

    Find the equation of the plane tangent to the graph of the function

    z(x,y) = 7(x^2) − 6(y^2) − 7x + 4y + 7 at the point (x,y)=(9,9)

    the z(x,y) is throwing me off since it isnt f(x,y). Is there any difference?

    I've done this problem about a million time, and am still not getting the right answer.

    my solution:
     z_x = 14x - 7
     z_x (9,9) = 14(9) - 9 = 119

     z_y = -12y + 4
     z_y = -12(9) + 4 = -104

    there is no value for z though which confuses me.

    I know that an equation of the tangent plane to the surface z = f(x,y) at the point  P (x_0, y_0, z_0) is
    z-z_0=f_x (x_0 ,y_0 )(x-x_0 ) + f_y (x_0, y_0)(y-y_0)

    but when I plug in everything into this equation I get  z = 119(x-9) - 104(y-9) which is wrong. Any help would be appreciated.
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  2. #2
    Super Member General's Avatar
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    Quote Originally Posted by rain21 View Post
    Find the equation of the plane tangent to the graph of the function

    z(x,y) = 7(x^2) − 6(y^2) − 7x + 4y + 7 at the point (x,y)=(9,9)

    the z(x,y) is throwing me off since it isnt f(x,y). Is there any difference?

    I've done this problem about a million time, and am still not getting the right answer.

    my solution:
     z_x = 14x - 7
     z_x (9,9) = 14(9) - 9 = 119

     z_y = -12y + 4
     z_y = -12(9) + 4 = -104

    there is no value for z though which confuses me.

    I know that an equation of the tangent plane to the surface z = f(x,y) at the point  P (x_0, y_0, z_0) is
    z-z_0=f_x (x_0 ,y_0 )(x-x_0 ) + f_y (x_0, y_0)(y-y_0)

    but when I plug in everything into this equation I get  z = 119(x-9) - 104(y-9) which is wrong. Any help would be appreciated.
    z(9,9) is the value of z.
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  3. #3
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    Quote Originally Posted by General View Post
    z(9,9) is the value of z.
    nvm solved it
    Last edited by rain21; January 30th 2010 at 05:58 PM.
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