Whipping one egg white in the KitchenAid mixer
I was disappointed when I first got my KitchenAid mixer that it doesn't do a very good job of whipping just one or two egg whites--in fact, sometimes it doesn't work at all. Here's my tip--use it carefully and at your own risk, as I would imagine that this is not recommended by the manufacturer.
To whip just one or two egg whites in my KitchenAid mixer, I cheat and tip the bowl a bit. I take one side off its little spike and tip it just the tiniest bit. Turn it on the lowest speed to make sure that the whisk does not hit the side of the bowl, but you will see that it actually picks up the egg whites now. When the whisk is adjusted so it doesn't hit the side of the bowl, you may increase the speed.