A competitive firm has the following short-run cost function: c(y) = y3 8y2 + 30y + 5.

A competitive firm has the following short-run cost function: c(y) = y3 ˆ’ 8y2 + 30y + 5.
(a) The firm€™s marginal cost function is ___________.
(b) The firm€™s average variable cost function is ___________.
(c) Average variable cost is falling as output rises if output is less than 4 and rising as output rises if output is greater than ______.
(d) Marginal cost equals average variable cost when output is _______.
(e) The firm will supply zero output if the price is less than _____.
(f) The smallest positive amount that the firm will ever supply at any price is _____. At what price would the firm supply exactly 6 units of output? ______.

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Costs 30 20 10