For any surface defined by f(x,y,z)= constant, is perpendicular to the surface at each point. You know how to find a plane given a point and normal vector?
Assume the tangent plane of the surface z = f(x,y) in the point (0,0,2) is given by z = Ax + By + 2. Find the equation for the tangent plane of the surface z = 1 / f(x,y) in the point (0,0,1/2).
No clue how to go about it. A hint or two, not a complete solution, would be appreciated.
For any surface defined by f(x,y,z)= constant, is perpendicular to the surface at each point. You know how to find a plane given a point and normal vector?