Answer: INTRAVENOUS CEFTRIAXONE
Explanation: To understand the question very well,let's critically look at the age of the infant and the presenting signs and symptoms.
The infant has a history of poor feeding,emesis(vomitting) and also there is history of irritability.there is also fever.when you look at all these,it is closely related to the signs and symptoms presented by infants with UTI ( urinary tract infection) but when you consider the vital signs of the infant (Temperature: 39.2°c, Respiratory: 40bpm,and Blood pressure: 80/50mmHg), the white blood cell count and the I'll looking appearance of the infant,
Upper tract disease that is (pyelonephritis) should be considered more because the signs and symptoms indicative of pyelonephritis are more strong than that of UTI.
Looking at the age of the infant and the severity of the presenting signs and symptoms, parenteral drug administration(intravenous/intramuscular) will act faster and will be easily absorbed and as well as easily accepted by the infant than enteral adminstration.
Looking at the options listed in the question,ceftriaxone is a third generation cephalosporin (a class of antibiotics used to treat varieties of bacteria infections) and it is so far the best drug in the treatment of pyelonephritis and also the best from the options given in the question,it's effectiveness is seen in the fact that it's gram negative coverage is excellent except in the case of pseudomonads where there is no encouraging gram negative coverage.