Final answer:
A curvilinear cost function can be graphed as a curved line within the relevant range. The average cost and marginal cost curves derived from the cost function also have the same shape.
Step-by-step explanation:
A curvilinear cost function can be graphed as a curved line within the relevant range. This means that the cost function does not have a constant rate of change, but instead varies as the input increases or decreases. For example, if the cost function represents the total cost of producing a certain quantity of goods, the curved line would show how the total cost changes as the quantity produced changes.
In addition, the average cost and marginal cost curves, which are derived from the cost function, tend to have the same shape as the cost function. This is because both average cost and marginal cost involve dividing the total cost by the quantity produced, and therefore their curves would also be curved lines.
Overall, the correct answer to the question is D. curved line.
The average cost and marginal cost curves are typically U-shaped curves, which first decrease and then increase. This happens because after a certain point, the cost of producing each additional unit starts to rise, reflecting the diminishing returns on the variable inputs in the production process. Hence, both the average cost curve and the marginal cost curve exhibit a 'U' form due to the behavior of costs in relation to production levels in the short run when at least one input is fixed.
By contrast, the long-run average cost curve reflects economies of scale and allows for all factors of production to change, differentiating it from the short-run average cost curve where fixed costs are present and only variable costs are allowed to change.