How to Improve Your Range
First and foremost, if you want to have great range on your brass instrument, you need to develop your stability. Your face needs to be working in an efficient and productive manner in terms of controlling the vibration of your lips. Most people (myself included) that have struggled with range have developed a certain habit in terms of how the muscles are coordinated in the face to make sound- and it doesn't work over the range we feel we need to do the job we want to do. This coordination has most likely also left certain muscles lacking the relative strength they need to 'hold' a certain setting or embouchure. The problem is two-fold. I look at it as 90% coordination and 10% strength. Follow the link below to learn more about stability- the best way to develop your range!
Now that you have learned about the importance of stability, here are some exercises I have used to increase my range.
Here is the ditto I used to keep track of my progress (Broken Intervals Template). Print as many times as you need. Remember the goal is to see how far down you can start from to still get the "high" note, so start filling in each row from right-to-left.
Range by 5's
Here is a second video where I demonstrate another exercise that will help to develop range.