According to the manual, [man]mime_content_type()[/man] is only available in PHP versions of 4.3+. Additionally, in order to make the function work PHP needs to have been configured with (built/compiled with) --enable-mime-magic (or --with-mime-magic since PHP 4.3.2).
Finally, you need to set an PHP.INI setting to properly find the mime "magic" file.
This is the default in PHP.INI
mime_magic.magicfile = "/usr/share/misc/magic.mime"
I think you are on the right track for solving your problem.