If the average total cost curve and the average variable cost curve are both U-shaped,and fixed costs are nonzero,then the minimum point of the average total cost curve must lie above the minimum point of the average variable cost curve.

The minimum point of the average variable cost curve corresponds to the point where the marginal cost curve intersects the average variable cost curve from below. Since the average total cost curve includes both variable and fixed costs, its minimum point will be higher than the minimum point of the average variable cost curve. This is because fixed costs are spread over a larger quantity of output as production increases, causing the average total cost to decrease at a slower rate than the average variable cost.