The correct response is:
The potential energy will stay the same as long as the book stays on the table. The kinetic energy increases when the book is shoved and then gradually decreases as it slides across the table and then comes to rest on the edge.
This explanation reflects that the book remains on the same level (table height), so its potential energy does not change. When the book is shoved, its kinetic energy increases as it starts to move, and it gradually decreases as friction slows it down until it comes to rest.