When a company produces and sells x thousands of units per week, its total weekly profit (in thousands of dollars) is The production level at t weeks from the present is x= 1 + 2t.

1. (5 points) The marginal profit is

   (a)
   
   (b)
   
   (c)
   
   (d)
   
   (e)
   
   (f)
   
   (g) none of the above

   Answer: (f)
   By the quotient rule,

   

2. (5 points) The rate of change of the profit with respect to time is:

   (a)
   
   (b)
   
   (c)
   
   (d)
   
   (e)
   
   (f)
   (g) none of the above

   Answer: (b)
   Note that . By the chain rule,