(disclaimer: I'm no expert in this, but I can report on )
The ASF draws a distinction between Apache-licensed software that is produced by the ASF, and your own software that is distributed under the Apache 2 license. The rules applied to the NOTICE change whether your software falls in one category or the other.
How should I apply the Apache License to my own software?
You should include a copy of the Apache License, typically in a file called LICENSE, in your work, and consider also including a NOTICE file.
It is also valuable to tag each of your source code files in case they become detached from the LICENSE file. To apply the Apache License to your source code files, one approach is to attach the following boilerplate notice to as a comment at the top of the files. You should replace the Copyright templates with your own identifying information: ...
If your project is not an apache project, you're not required to even keep a NOTICE file.
The NOTICE file is a good place to mention if certain parts of the code have different copyright, or if certain parts are under different a different license. The LICENSE file should remain unmodified, straight from the official license.
According to this page, https://www.osehra.org/wiki/how-apply-apache-20-license-your-software-project , the NOTICE should be used to identify the following information:
- The copyright holders (and potentially patent holders)
- The portions of the source code for which they hold the copyright (and that potentially can be covered by their patents)
- The License adopted for that portion of the code
Whether or not you consider OSEHRA to be an authoritative source for that kind of information, you should keep the NOTICE short, because it will need to be redistributed by "downstream" users of your software (that's rule 4d of the license). i.e. don't add anything to the NOTICE that isn't legally relevant.
Regarding your specific example
Your question asks about the validity of the following the specific notice text:
This product includes software developed at
The Apache Software Foundation (http://www.apache.org/).
If your code wasn't developed at the Apache Software Foundation, then I wouldn't write that in the notice. It would be false information. Perhaps this was obtained from an example NOTICE only applicable to new software projects specifically from the ASF?