Question

Suppose that the total cost function, in dollars, for the production of x units of a...

Suppose that the total cost function, in dollars, for the production of x units of a product is given by the equation shown below.

C(x) = 17640 + 65x + 0.4x2

Then the average cost of producing x items is represented by the following equation.

C(x) = total cost = 17640 + 65 + 0.4x
x x

(a) Find the instantaneous rate of change of average cost with respect to the number of units produced, at any level of production.

C'(x) =



(b) Find the level of production at which this rate of change equals zero.
x =

(c) At the value found in part (b), find the instantaneous rate of change of cost and find the average cost.

instantaneous rate of change of cost
average cost


What do you notice?

The instantaneous rate of change of cost equals the average cost.The instantaneous rate of change of cost is greater than the average cost.    The instantaneous rate of change of cost is less than the average cost.

Math   Calculus   
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