Explain why the marginal cost curve intersects the average cost curve at its minimum point?

Marginal cost (MC) is the extra cost incurred when one extra unit of output is produced. Average product (AC) is the total cost per unit of output. When the MC is smaller the AC, the AC decreases. This is because when the extra unit of output is cheaper than the average cost then the AC is pulled down. Similarly, when the MC is greater than the AC, the AC is pulled up. The point of intersection between the MC and AC curves is also the minimum of the AC curve. This can be explained by the fact that when the cost of the marginal output is equal to the average cost of the output, then the AC neither falls nor rises (i.e. it reaches its minimum).