Using the IIS namespace, one can query the IIS Apppool settings, using:
$pools = get-wmiobject -namespace "root/microsoftiisv2" -query 'select * from IIsApplicationPoolSetting'
However, this only returns information about the existing application pools.
How can one query the current application pool defaults, the same that are retrieved from Application Pools > Set Application Pool Defaults
. These values are different from the Default Application Pool (DefaultAppPool)
The following should get you started: