I think it applies to your case. You have to prove to the Department of State that you automatically derived citizenship through your parent/s. The way to prove it is the GC, your parent naturalization certificate and proof to satisfy that you were living in the USA under the legal and physical custody of your parent before you turned 18.
The way you have explained your case so far it shouldn't be too difficult to gather enough proof.
In general, it is much easier if parents take care of this before the child turns 18. In my child's case it was a simple affair, both parents and child showed up at post office with GC, birth certificate and naturalization certificate. The passport acceptance agent processed all our three applications with just two naturalization certificates (by making a certified copy of one of the certificates). No need for school records, medical records or anything else, as in this case the child is still under 18 and clearly under the legal and physical custody of the parents who are showing up at the post office. Your case is slightly more involved, but not much more. Worse comes to worse the passport acceptance agent will tell you if something is missing. Even in the worst case the passport agency will ask you for any additional evidence. Please let us know how it goes.