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Word Problems : Derivatives and Rate of Change

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41) Suppose that the average yearly cost per item for producing x items of a business product is C(x)=10+(100/x) . if the current production is x=10 and production is increasing at a rate of 2 items per year, find the rate of change of the average cost.

45) Suppose a 6ft tall person is 12 ft away from a 18-ft tall lamppost. if the person is moving away from the lamppost at a rate of 2 ft/s, at what rate is the length of the shadow changing? (Hint: show that (x+s)/18=s/6.)

47) Suppose that a raindrop evaporates in such a way that it maintains a spherical shape. given that the volume of a sphere of radius r is V=(4/3)(phi)r², if the radius changes in time, show that V'=Ar'. If the rate of evaporation (V') is proportional to the surface area, show that the radius changes at a constant rate.

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