Many doctors rely on the use of intravenous medication administration in order to achieve an immediate response of a particular drug's effects. The concentration C in mg/L of a particular medication after being injected into a patient can be given by the function C(t) = -10t^2 + 50t/ t^2 + 4t+3, where the time, t, is hours after injection. Part A: What is the domain of the function C(t) based on the context of the problem? Show all necessary calculations.
Part B: Graph the function to determine the greatest concentration of the medication that a patient will have in their body.