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Attempts Keep the Highest $/4$

$3.$ The relationship between marginal and average costs

The following scenario examines the relationship between marginal and average values. Suppose Diego is a high school basketball player. The following table presents their game$-$by$-$game results for foul shots.

Fill in the columns with Diego's foul$-$shooting percentage for each game and their overall foul$-$shooting average after each game.

On the following graph, use the orange points $($square symbol$)$ to plot Diego's foul$-$shooting percentage for each game individually, and use the green points $($triangle symbol$)$ to plot Diego's overall average foul$-$shooting percentage after each game.

Note: Plot your points in the order in which you would like them connected. Line segments will connect the points automatically.

Game Foul$-$Shooting Percentage

Average Foul$-$Shooting Percentage

You can think of the result in any one game as being Diego's marginal shooting percentage. Based on your previous answer, you can deduce that when Diego's marginal shooting percentage is below the average, the average must be

You can now apply this analysis to production costs. For a U$-$shaped average total cost $($ATC$)$ curve, when the marginal cost curve is below the average total cost curve, the average total cost must be $.$ Also, when the marginal cost curve is above the average total cost curve, the average total cost must be $.$ Therefore, the marginal cost curve intersects the average total cost curve $..$