Which of these does Amazon RDS NOT handle for you?

RDS does not index your tables or tune slow queries. That stays your job.

RDS manages the infrastructure side:
• Creating the database servers.
• Backups and point-in-time restore.
• Patching the engine in a maintenance window.
• Monitoring.
• Failover to a standby in Multi-AZ.

Schema design, indexes and query speed stay with you. A managed database is still slow if indexes are missing.