Economics—Profit Function: The Network Standards Company has determined from data that it...

Economics—Profit Function: The Network Standards Company has determined from data that it has collected that its profit function for its new E1020 routers is given by

 P(x) = 1000x − 2x2 0 ≤ x ≤ 300

where x represents the number of routers produced and sold and P(x) represents the profit in dollars.

(a) Use the definition of derivative to determine P′(x), where .

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(b) Use the result of part (a) to compute P′(200) and P′(300) and interpret each using appropriate units.