How can I transform one end of a cylindrical extrusion to create a cone or needle-like structure? I have a mesh with a cylindrical extrusion and I would like to make this extrusion appear like a cone or needle.  I have tried scaling the end faces/edges/verts of the cylinder, but this scales the entire mesh.  I do not want to scale the entire mesh.

Before:

+================+
|                |
|                +=============================+
|                                              |
|                           cylinder           |         
|                                              |
|    (mesh)      +=============================+
|                |
+================+


Desired result:

+================+
|                |
|                +=============+
|                               ========+                
|                   needle/cone          ======             
|                               ========+              
|    (mesh)      +=============+
|                |
+================+


Yes, I'm in Edit Mode and, yes, pivot center is set to Median Point.

Here's a screencast of what is happening.
You are either in Object Mode or have the whole mesh selected.

Make sure that you are in Edit Mode (Tab). In the header of the 3D View:



Then press A repeatedly until nothing is selected. Then use border select (B) for example to select the right most vertices:



Then scale them down. It might be that you have to change your pivot point to Median Point.
Again in the 3D View header:



You also have to make sure that proportional editing is off (O) (header again).