Explain why the short-run marginal-cost curve must intersect the short-run average-total-cost curve at the minimum point of

Question:

Explain why the short-run marginal-cost curve must intersect the short-run average-total-cost curve at the minimum point of the ATC. Does the marginal-cost curve intersect the average-variable cost curve at its minimum point? What about the average-fixed-cost curve? Why doesn’t the marginal-cost curve also intersect the average fixed-cost curve at its minimum point?

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