2.99
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When a company produces and sells x thousand units per week, its total weekly profit is P thousand dollars, where

P = 200x / (100 + x2).

The production level at t weeks from the present is x = 4 + 2t.

(a) Find the marginal profit, dP/dx.

(b) Find the time rate of change of profit, dP/dt.

(c) How fast (with respect to time) are profits changing when t = 8?