1. For each of the following statements, determine Whether the statement is true or false (the latter including \"not necessarily true\"), and provide a brief explanation. (a) If a production function f (1:) With one input :1: increases until 20 and decreases thereafter, then the rm's marginal product is increasing if and only if :19 20. (c) It a rms' average cost is decreasing at y then its marginal cost is also decreasing at y. (d) If the marginal cost is decreasing until 10 and then increasing, then the average cost is minimized at :L' = 10