Find the equation of the tangent plane at (3,4,1) to the surface x^2+y^2-xyz=13. View the surface as the graph of a function of two variables z=g(x,y).
Find the equation of the tangent plane at (3,4,1) to the surface x^2+y^2-xyz=13. View the surface as the graph of a function of two variables z=g(x,y).
I did not check to see if that point is on the surface.
$\displaystyle \Delta F(x,y,z)=<2x-yz,2y-xz,-xy>$
Now the tangent plane is:
$\displaystyle \Delta F(3,4,1)\cdot <x-3,y-4,z-1>=0$