What is the maximum age of a non-working child to be able to claim him as a dependent of a Federal Tax return?

There is no age limit.
Your child can be your dependent as your Qualifying child (if under 19) or as Qualifying Relative (no age limit). Your U.S. Tax Return: Requirements for claiming a dependent

You may wish to read the rules regarding dependents starting on page 11, see the chart:
http://www.irs.gov/pub/irs-pdf/p501.pdf