US: If you have a built-in fuel tank, a space where fuel vapors can build up (try interpreting that one) or a boat longer than 26 feet, you are required to have at least one extinguisher. They suggest it be mounted, but their requirement is actually that it be readily available (in a locker under all the PFD's doesn't work.
I'd say on the transom, probably opposite your pillot's seating. Only thing that's going to be an issue on a small inflatable is the engine, so keep the extinguisher nearby.
On a larger boat, you can add the electrical system into the mix. An extinguisher is unlikely to help a whole lot in this case, unless you can kill power to the problem area.
To be honest, I've used two extinguishers on my boat: one was to cool off an overheating trailer drum (corroded, broken and jammed brake lining), and once to pass off to another boat who was having problems. Odds of having a fire on board aren't really all that high, assuming you do a reasonable amount of maintenance.
I'd suspect you'd be fine tubing, but you probably want to make your take-off as smooth as possible, and limit your extreme whips. That's just a guess, though.