Why does the marginal cost curve cross the average total cost curve at the minimum of the average total cost?

Marginal cost curve is lower than the average total average cost curve because the cost of additional output is lesser than the average cost; so average cost is pulled downward. When the marginal cost is more than average cost, average cost curve is pulled upward. Therefore, when marginal cost and average cost is equal, average cost curve neither increase nor decrease, it is at minimum. Hence, the marginal cost curve cross the average total cost curve at the minimum of the average total cost.

Therefore, marginal cost curve crosses the average total cost curve at its minimum point because the marginal cost of producing the next unit of output will always influence the average total cost.