Find the equation of the tangent plane to the surface determined by
(x^4*y*2)+z−20=0

at x=2, y=2.

z=

Question

Find the equation of the tangent plane to the surface determined by
(x^4*y*2)+z−20=0

at x=2, y=2.

z=

anonymous · Answer

i think this looks like example 1 here http://tutorial.math.lamar.edu/Classes/CalcIII/TangentPlanes.aspx

anonymous · Answer

we can try it if you like

anonymous · Answer

start with 
$$z=20=x^4y^2$$ that is the equation right?  then at x = 2, y = 2 you get 
$$z = 20-64=-44$$
$$f_x=-4x^3y^2$$ and 
$$f_y=-2x^4y$$ at x = 2, y = 2 you get 
$$f_x=-128$$
$$f_y=-64$$ and the plane will be 
$$z+44=-128(x-2)-64(y-2)$$ and then some algebra should complete it

anonymous · Answer

of course i could be way wrong, so i wouldn't bet money on this

anonymous · Answer

Thats exactly correct!  Thanks for the help

anonymous · Answer

I appreciate the work you showed so I could follow the steps