IMHO, Warm up nicely. Do octave slurs, i.e. E to E back down to E, F to F back to F, F# to F# back to F#, etc., playing 1/4 notes at about a 100 meter, REST 20 to 30 seconds between each octave slur.........when you reached you maximum range for the day (only try twice, if you do not hit the top note after 2 trys....time to put the horn away) Do the same routine the next day. You should be able to extend your range with patience and persistance.
This a good method that works for me except I try to play the note 3 times. I believe that was the Claude Gordon method. Also, try to play in the higher range if that is what you plan on doing. The key to the above method is resting between the octaves. and, you need breath support. You can't play any high notes, regardless of how talented you are, if you do not support the breathing.