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 accurately describes the changes in potential and kinetic energy during the process. While the book is on the table, its potential energy remains constant since the height hasn't changed. When the person shoves the book, its kinetic energy increases as it gains speed, and then it gradually decreases due to friction until it comes to rest.