A competitive firm has the following short-run cost function: c(y) = y^3-8y^2+30y+5.
a) find the firm's marginal cost function
b) find the firm's average variable cost function
c) graph the marginal cost function and the average variable cost function
d) find the level of output when marginal cost equals average variable cost
e) at what price the firm will supply zero output
f) at what price the firm will supply the smallest positive amount? At what price would the firm supply exactly 6 units of output?