Final answer:
The most suitable task for a public health nurse is teaching a client how to self-administer insulin as it relates to health education and disease prevention, key components of public health.
Step-by-step explanation:
The task most appropriate to assign to a public health nurse would be teaching a client how to self-administer insulin. This aligns with the role of public health professionals who are involved in health education and disease prevention interventions. A public health nurse would implement strategies designed to manage chronic conditions like diabetes, which includes educating patients on proper self-care techniques. Certified diabetes educators, who often come from a nursing background, specialize in teaching patients to manage their diabetes through self-monitoring of blood sugar levels, diet, exercise, and medication management.