Which of the following is a sign of possible meningitis in an infant?

Bulging fontanelle and irritability are significant indicators of potential meningitis in an infant. The fontanelles are the soft spots on an infant's skull that allow for brain growth and development. When there is increased intracranial pressure, such as that which can occur with meningitis, the fontanelle may protrude or bulge outward. Complementing this physical sign, irritability is often observed in infants suffering from meningitis, as they may be uncomfortable and in distress due to the inflammation and pressure in their central nervous system.

While other symptoms mentioned in the other options can be relevant to various illnesses or infections, they are less specific indicators of meningitis compared to the combination of a bulging fontanelle and irritability. For instance, a rash and fever can also indicate a range of conditions, including viral infections or other febrile illnesses. Persistent vomiting and diarrhea may signal gastrointestinal issues, and lack of appetite and sleepiness can be symptoms of numerous childhood ailments but lack the neurological specificity seen in the signs of meningitis. Thus, the presence of both a bulging fontanelle and irritability particularly directs attention toward the possibility of meningitis.