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*).