essay

Question
The cost (in dollars) of producing x units of a certain commodity is C(x) = 5000 + 10x + 0.05×2.
(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
(ii) from x = 100 to x = 101

(b) Find the instantaneous rate of change of C with respect to x when x = 100. (This is called the marginal cost. Its significancewill be explained in Section 3.7.)

156.

Question

A warm can of soda is placed in a cold refrigerator. Sketch the graph of the temperature of the soda as a function of time. Is the initial rate of change of temperature greater or less than the rate of change after an hour?