A mobile app for booking doctor appointments is running very slowly when accessing data from a database and the programmers think that poorly optimised SQL statements are causing it. There are three places where they think the code might be slow.

1. When users book a new appointment.

2. When the date of an appointment is modified.

3. When a user searches for doctors by name or specialty.

Could any of these be improved by creating a database index? Why/Why not? What column or columns (if any) would be appropriate to add an index to?