All the database connections are logged during server 
startup in the server logs.

you can get the connection details by executing netstat -a 
| grep <ipaddress of DB Server

in admin console you can go to the JDBC->connection pool-> test
it will test the pool and display the result, if the
application is connected to the db it will show a test
successful message else error

1.In admin console you can go to the JDBC->connection pool-> 
You will find status as running if DB is up i.e connected.

And to be more confident
       JDBC->connection pool-> test

- Test connection successfully ( test connection attributes
in the advance configuration of the connection pool should
be checked and there should be a dummy table -- "dual" is by
default)
- If "Test connection" attributes are not checked then a
warning will appear.

2. If a DB connection is not available , you can find
related message in the server logs also.