According to the author of the book, the story shows that David understood something was wrong when he saw his servants talking quietly. He realized that his child had died and asked the servants, and they confirmed it.
2 Samuel 12:19: But when David saw that his servants whispered, David perceived that the child was dead: therefore David said unto his servants, Is the child dead? And they said, He is dead.
This verse acknowledges that David realizes he cannot bring his child back and shows acceptance, whereas 2 Samuel 12:19 shows David moving past mourning upon realizing his child has died.
2 Samuel 12:23: But now he is dead, wherefore should I fast? can I bring him back again? I shall go to him, but he shall not return to me.