How come os shows 6.5G used but I see only 3.6G in files/directories?

Running as root on an Amazon Linux AMI (seems like Centos), lots of free memory available, no swapping going on, no apparent file descriptors issue. The only thing I can think of is a log file that was deleted while applications append to it.

Disk space usage is slowly but continuously rising towards full capacity (~1k/min with very small decreases from time to time)

Any explanation? Solution?

du --max-depth=1 -h /
1.2G /usr
4.0K /cgroup
22M /lib64
11M /sbin
19M /etc
52K /dev
2.1G /var
4.0K /media
0 /sys
4.0K /selinux
du: cannot access /proc/14024/task/14024/fd/4': No such file or directory du: cannot access<br/> /proc/14024/task/14024/fdinfo/4': No such file or directory du:
cannot access /proc/14024/fd/4': No such file or directory du: cannot<br/> access/proc/14024/fdinfo/4': No such file or directory 0 /proc
18M /home
4.0K /logs
8.1M /bin
16K /lost+found
12M /tmp
4.0K /srv
35M /boot
79M /lib
56K /root
67M /opt
4.0K /local
4.0K /mnt
3.6G /

df -h

Filesystem Size Used Avail Use% Mounted on
/dev/xvda1 7.9G 6.5G 1.4G 84% / tmpfs 3.7G 0 3.7G 0% /dev/shm

sysctl fs.file-nr fs.file-nr = 864 0 761182