A quick technique tip:
The common mistake that students make in the third octave is simply overblowing the fingerings one and two octaves lower. The technique may come more easily this way, but the pitch, response and tone are poor. It only takes one flutist (or worse yet, piccolo player) in a flute section playing the overblown fingerings to cause a very annoying pitch problem in the upper register of an ensemble.
--From "Band Director Talk Shop," Nov. 7, 2017. Adapted from Woodwind Methods: An Essential Resource for Educators, Conductors, and Students by Charles West