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Mathematics, 15.04.2020 23:23 mtolds1952

The production function f(x) gives the number of units of an item that a manufacturing com pany can produce from units of raw material. The company buys the raw material at price w dollars per unit and sells all it produces at a price of p dollars per unit. The quantity of raw material that maximizes profit is denoted by x*.

(a) Do you expect the derivative f'(x) to be positive or negative? Justify your answer

(b) Explain why the formula π(x) = pf(x) - wx gives the profit π(x) that the company earns as a function of the quantity x of raw materials that it uses.

(c) Evaluate f'(x*).

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