The middle range on the sax is relatively easy to play compared to the bottom few notes and the upper register. While the very low end can be fixed by simply applying much more air support, getting the highest notes to play strong and in tune can be a bit more complicated than that.
Sometimes, and depending on what stage of development you’re in, it’s not just about changing reeds or getting a better mouthpiece. Ok, there’s the bad news, the goods news is that you have the necessary tools to improve your flat and thin high notes already with you.
Producing a nice sound in that upper range can be a little difficult to say the least for a new student. At the beginning we don’t have good control over our embouchure. When reaching for those higher notes it’s natural to slip back on the mouthpiece, meaning less of it is in your mouth. We tend to bite hard as well and less air is being pushed through from the diaphragm, where it should be blasting out from.