Tangent plane equation of surface x ^ 2 + 2Y ^ 2 + Z ^ 2 = 12 at point (1,1, - 3)
Let f (x, y, z) = x ^ 2 + 2Y ^ 2 + Z ^ 2;
F'(x)=2x;F'(y)=4y;F'(z)=2z;
The normal vector of the tangent plane at (x0, Y0, Z0) is (2x0,4y0,2z0);
So the tangent plane equation at (x0, Y0, Z0) is 2x0 (x-x0) + 4y0 (y-y0) + 2Z (z-z0) = 0;
Just bring in the point coordinates
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