The cost (in dollars) of producing x units of a certain commodity is C(x) = 7000 + 6x + 0.15x2. (a) Find the average rate of change of C with respect to x when the production level is changed from x = 100 to the given value. (Round your answers to the nearest cent.) (i) x = 103 $ per unit (ii) x = 101 $ per unit (b) Find the instantaneous rate of change of C with respect to x when x = 100. (This is called the marginal cost.) $ per unit

The instantaneous rate is 36.

Step-by-step explanation:

Given the cost of producing a commodity,

Now calculate the average rate of change in cost of producing commodity.  

Use below formula to calculate average rate of change when (i) x = 103 $ per unit:

Now calculate average rate of change when (ii) x = 101 $ per unit:

Now to find the Instantaneous Rate of Change we just need to find the differentiation of given function.

Instantaneous Rate of Change when x = 100