The average cost per item to produce [math] items is given by [math]

What is the total cost, [math], of producing [math] goods?
[math]

What is the minimum marginal cost?
minimum MC =
(Be sure you can say what the practical interpretation of this result is!)

At what production level is the average cost a minimum?
[math]
What is the lowest average cost?
minimum average cost =

Compute the marginal cost at [math].
[math]
How does this relate to your previous answer? Explain this relationship both analytically and in words.