Find an equation for the tangent plane to the surface x^2+y^2-z=0 at the point (1,1,2).
Your solution will be of the form , where are constants.
Note that are simply the coordinates of . So, your solution will look something like this:
We want to find the constants a, b, and c. How? We first compute the partial derivatives of our surface equation .
The gradient vector is given by:
Then, plugging in the coordinates of , we get:
So0oo, the constants , respectively.
Soooooooo, the equation for the tangent plane to the surface is
Rearrange this if you so wish.