The correct answer is A) a high viscosity index. A lubricating oil with a high viscosity index is better suited for a diesel engine exposed to widely varying ambient temperatures. This is because a high viscosity index indicates the oil's ability to maintain its viscosity (thickness) over a wide range of temperatures. This helps ensure proper lubrication and protection of engine components, even as the ambient temperature fluctuates. The other options are incorrect because: B) a low viscosity index would not provide sufficient protection in varying temperatures, C) extreme pressure additives are not specifically required for this situation, and D) the engine requires a lubricating oil with additives to perform well under changing conditions.