The cost (in dollars) of producing [math] units of a certain commodity is [math]

(a) Find the average rate of change of [math] with respect to [math] when the production level is changed

(i) from [math] to [math].
Average rate of change =

(ii) from [math] to [math].
Average rate of change =

(b) Find the instantaneous rate of change of [math] with respect to [math] when [math]. (This is called the marginal cost.)
Instantaneous rate of change =