Question

The cost (in dollars) of producing x units of a certain commodity is
C(x) = 3500 + 7 x +0.3 x^2.


(a) Find the average rate of change of C with respect to x when the production level is changed
(i) from x = 100 to x = 105.

Average rate of change =

(ii) from x = 100 to x = 101.

Average rate of change =
(b) Find the instantaneous rate of change of C with respect to x when x = 100. (This is called the marginal cost.)

Instantaneous rate of change =