Final answer:
To dynamically show additional fields when a record's field value changes, an application developer should use a workflow to change the record type. This process will update the page layout and make the new fields visible without directly altering field-level security or needing multiple Visualforce pages.
Step-by-step explanation:
The student has presented a scenario about dynamic field visibility on a record in response to a change in the value of a field. In this case, when the value of the Stage field on a record of Object X changes from 'New' to 'Working', additional fields should become visible to the user.
Among the options provided, the most suitable way for an application developer to configure this behavior is to use workflow to change the record type. Workflows can automate this process by updating the record's type when the Stage field is changed, which can then change the page layout and expose additional fields to the user. This method does not involve direct manipulation of field-level security, validation rules are not designed to control field visibility, and using multiple Visualforce pages is more complex and less maintainable than changing the record type through a workflow.