Suppose you have a single variable differentiable function r: R -> R restricted to an interval, like [0,1] for simplicity, if you want. Consider the surface of revolution obtained by rotating the graph of r around the x axis. How do I find the NORMAL VECTOR to the surface at each of its points (x,y,z)? I guess I could find the normal vector to the graph of r in the xy plane and then rotating it with the same rotation I use to generate the surface of revolution. Somehow though this process seems to become unfeasible at some point so I must be missing something or doing it the wrong way altogether.