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In economics, the notion of concavity is related to the concept of diminishing returns. Consider a function y = f () where x measures input (in dollars) and y measures output (in dollars). In the graph, notice that the graph of this function is concave upward on the interval (a,c) and is concave downward on the interval (c,b). On the interval (a,c), each additional dollar of input returns more than the previous input dollar. By contrast, on the interval (c,b), each additional dollar of input returns less than the previous input dollar. The point (c, f (c) ) is called the point of diminishing returns. An increased investment beyond this point is usually considered a poor use of capital. Concave downward Output (in dollars) Concave upward Point of diminishing returns Input (in dollars) Find the point of diminishing returns for the model below, where R is the revenue (in thousands of dollars) and x is the advertising cost (in thousands of dollars): 20,000 (450x2 - 23) , 0