You are able to configure that. If you grant your account the "auditing configurator" role in RBA, then from the core server launch the console. With-in the console click on Configure -> Services. Then select the audit tab that will now appear.
You can then choose which actions you wish to log from here.
I will warn you though that Scheduled Task auditing is very noisy. Our DBs would grow by an additional 50-100gb over the course of 1-2 months just from the Schedule Task auditing being enabled. After doing research we determined 99% of this was from the Scheduler Service account updating tasks on its own and portal tasks. It edits and starts tasks all the time. So if you enable either of those two options, I would highly recommend adding a SQL job that runs every night to drop the service accounts scheduled task history.
We use this sql command in our sql job to do this and keep the DB slim:
delete from AuditInstance where Username like '%accountnamehere%' and FeatureEvent like '%Scheduled Task'
You can then view these logs from the console under:
Hope this helps,
I have configured the auditing as you describe. That's great for moving forward. Is there any way to determine when in the past a task was deleted, and/or who did it?
Re: "Is it possible to see who deleted it In the past" ... if it was audited at the time - yeah,
If it wasn't audited at the time -- then no, not really.