Final answer:
Increased urine output suggests that a client receiving TPN has developed hyperglycemia, as elevated glucose levels lead to more urine being excreted by the kidneys.
Step-by-step explanation:
A nurse assessing a client who is receiving total parenteral nutrition (TPN) and looks for signs of hyperglycemia should note that an increased urine output is a potential indicator. This condition can occur if the high levels of glucose in the blood lead to an osmotic diuresis, causing the kidneys to excrete more urine. This symptom is one of the classic signs of diabetes mellitus, where blood glucose levels are elevated, and similarly can indicate hyperglycemia in a patient receiving TPN.