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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