Step 1: Understand the relationship between Marginal Cost (MC) and Average Cost (AC).
- If MC is less than AC, AC falls.
- If MC is greater than AC, AC rises.
- If MC equals AC, AC reaches its lowest point.
Step 2: Apply this principle to the problem.
The marginal cost curve intersects the average cost curve precisely at the average cost's minimum.
Final Answer: \[\boxed{\text{At the minimum of the average cost curve.}}\]