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51

Step-by-step Answer
PAGE: 116SET: ExercisesPROBLEM: 51
Please look in your text book for this problem Statement

Cost of producing  units of a certain commodity is 

(a)

Average rate of change of  with respect to :

(i)

when production level is changed from  to :

Cost of producing  units is .

Cost of producing  units is .

 Average rate of change of  from  to  is 

Average rate of change of  from  to  is  dollars/unit.

(ii)

When production level is changed from  to :

Cost of producing  units in that commodity is .

Cost of producing  units in that commodity is .

 Average rate of change of  from  to  is 

 Average rate of change of  from  to  is  dollars/unit.

(b)

Instantaneous rate of change of  with respect to  when :

The derivative  is the instantaneous rate of change of  with respect to  at .

Instantaneous rate of  change 

Here .

Let 

Instantaneous rate of change of  when  is  dollars/unit. 

(a)

(i)  Average rate of change of  from  to  is  dollars/unit.

(ii)  Average rate of change of  from  to  is  dollars/unit.

(b)

Instantaneous rate of change of  when  is  dollars/unit.



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