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The cost function is already given as C(x) = 1/2 * x^2.

To find the average cost function, we will divide the cost function by the quantity x. Therefore, AC(x) = C(x)/x = (1/2 * x^2)/x = (1/2) * x

To find the marginal cost function, we will find the derivative of the cost function with respect to x: MC(x) = d(C(x))/dx = d(1/2 * x^2)/dx = x

Now that we have the cost, average cost, and marginal cost functions, we can graph them to visualize their relationships. Plot the functions C(x), AC(x), and MC(x) on the same graph with x on the horizontal axis and C(x), AC(x), and MC(x) on the vertical axis. The graph will show that: 1. The cost function C(x) is a parabola, opening upward, indicating that the cost increases with increasing production. 2. The average cost function AC(x) is a straight line with a positive slope, showing that the average cost per unit increases with increasing production. 3. The marginal cost function MC(x) is also a straight line with the same slope as the average cost function, which means that the additional cost to produce one more unit is constant for every level of production.

The key idea behind diminishing returns is that as production increases, the additional benefits from that production start to decrease, while the additional costs continue to increase. As a result, the efficiency of producing more goods decreases, leading to an increase in the average cost per unit. In the context of this exercise, the increasing average and marginal costs shown in the graph support the idea of diminishing returns. As production (x) increases, both average and marginal costs increase, meaning that producing additional units becomes less and less efficient. In summary, the diminishing returns concept is reflected in the cost function C(x) = 1/2 * x^2, as the increasing production level (x) leads to an increase in average and marginal costs, which in turn indicates decreasing efficiency in the production process.