The physics is fairly simple. It takes a fair bit of lung pressure to play even a quiet high C - typically 30" water gauge (WG) though this value seems to vary a bit with individual and experience. And your embouchure has to be strong enough to withstand that pressure without your aperture blowing open. To play either a louder high C, or a quiet high D, you need significantly higher lung pressure, and therefore significantly more strength in your embouchure. And so on. Add to this the complex microadjustments of aperture size and lip tension required to ensure you get a clear high C rather than a quiet D (or loud Bb!), all of which have to operate in synchrony without you having to think about them, and you get some idea of why relatively small improvements in range take many months of properly structured, regular practice to achieve. This is where lip slurs really come into their own. As a regular part of your practice routine, they both build the embouchure strength, and over many thousands of repetitions, lock in the muscle memory so that you can replicate the exact physical set up required for that note no matter what distance and direction you approach it from. Oh yes, and you have to get your abdominals working in synchrony too. And I'm not even going to mention the tongue. Oops.