Mapping stat(1) device number/name to partition?

[Rick van der Zwet]

Hi all,

I am looking for a way to detect the file system a certain file lives
and next whether this file system is mounted/accessible as writable. [1]

As stat(1) is helping me out to found out the proper device name/number
of a certain file with the command `stat -f "%d" /etc/motd`, but next
will be the mapping from this device number (st_dev) to the proper
partion/mount point.

Which handy shell utility program will help me doing this?

Or even better what are the proper search terms to find this answer, as
mine attempts on the mailing archives, man pages and Google where not
very successful

Thanks a lot!
/Rick

[1] Part of getting rid of the annoying motd update failure message,
    when /etc is not writable. I know setting update_motd=NO in
    /etc/rc.conf will do the trick as well, but I would like to see him
    detecting it auto-magically ;-)