The parents demonstrate understanding when they state that which of the following behaviors indicates that an infant has developed object permanence?

The correct answer is C because actively searching for a hidden object indicates that the infant understands object permanence, the concept that objects continue to exist even when not in sight. This behavior shows that the infant knows the object exists even when it is out of sight. Choices A, B, and D do not specifically demonstrate object permanence as they could be based on other cognitive abilities like recognition or motor skills. Therefore, only choice C directly correlates with the development of object permanence in infants.