Final answer:
In the presence of a depressed respiratory rate and central cyanosis in a newborn infant, administering oxygen is the correct and immediate treatment necessary to address the infant's need for oxygenation, especially in conditions like Respiratory Distress Syndrome (RDS).
Step-by-step explanation:
If a newborn infant's respiratory rate is depressed and central cyanosis is present, you should administer oxygen. This is the primary intervention in this scenario because it addresses the immediate need for oxygenation. Respiratory Distress Syndrome (RDS) is a common condition in premature infants, and can lead to insufficient breathing effort and poor oxygen intake. At delivery, lifesaving measures may include resuscitation and intubation if necessary, often followed by mechanical ventilation or nasal CPAP to support breathing.
The administration of pulmonary surfactant can also significantly reduce mortality rates in these cases. Other supportive therapies may involve temperature control, nutrition, and in cases where infection is a concern, antibiotics. However, without immediate oxygenation, the risk of further hypoxemia and potential damage increases. Pain medication and antipyretics are not appropriate as initial treatments for respiratory depression and cyanosis in newborns.