componets in your sub floor and where they are located and what has happened to cause this dip.
If the house is a pier and beam, the dip is most likely between two parrellel floor joists that could be make of particle board of some sort and could have been wet at one time and caused it to loose its rigidity and dip.
Once you open this area up, you will be able to tell what happened. Once you do, you can readily fix this by cutting out a larger square piece of the sub flooring and installing a new square in that area. You want to make sure to use the floor joists as your nailing board and use the sistering method to make new nailing boards. Use screws of rust resistant material and many screws.
Your problem is not uncommon and usually occurs around areas that have water being used, for instance comodes, sinks, washing machines, and garbage disposals that at some time will leak or flood.
Make sure your patch is the same width as the existing floor.