Some cities and other local governments require that smoke detectors be placed inside every bedroom, as well as outside of sleeping areas on every floor. If your home does not have these, you could be putting your family at risk. Outside of sleeping areas, it is recommended that smoke detectors be installed near a stairway, in the basement, and near cooking appliances.
Whether a fire extinguisher is legally required in your home will be determined by your local or state code. You should make sure to have one regardless of law, but if your landlord has not provided a fire extinguisher, you should look up your local ordinances to find out if they are required to provide one, and have it placed in an easily accessible area.