Why does the marginal cost curve cut the average cost curve at its lowest point?

The marginal cost is the additional cost to produce an additional unit of output. The average cost is calculated by dividing the total cost by the quantity of output. The marginal cost (MC) of producing an additional unit of output will affect the average total cost (AC) in the following way, such as:

(i) If MC > AC then AC will be rising.

(ii) If MC < AC then AC will be falling.

(iii) And then MC = AC, only when AC is at the lowest point.

Thus, the marginal cost curve intersects average cost curve, i.e., MC = AC only at the lowest point of the average cost curve.