Let the cost function of a firm beC(x)

C(x), the average cost beC(x)

x

C(x)x, and the marginal cost beC

(x)

C(x). Prove that the average cost is minimized only when marginal cost equals the average cost. What other condition needs to be satisfied for the average cost to be the minimum? (Assume continuity and differentiability of relevant functions wherever required.)