Find all points on the surface at which the tangent plane is horizontal
Things I know:
Tangent plane is horizontal then therefore the normal must be vertical in order to be perpendicular.
Dot product of the tangent plane with normal is = 0
Normal plane is given by the partial with respect to x,y,z evaluated at some points P(x0,y0,z0)
Putting that together I get
Here is where I am completely stuck I know that I still don't have a normal vector because I do not have any points to plug in to the partials.