Suppose total cost in dollars from the production of x printers is given by c (x) = 0.0001x3 + 0.005x2 + 28x + 3000. (a) find the average rate of change of total cost when production changes from 200 to 300 printers. incorrect: your answer is incorrect. (b) find the average rate of change of total cost when production changes from 300 to 500 printers. incorrect: your answer is incorrect.

Determine the rate of change of the total cost by deriving the equation.

dc (x) / dt = 3 (0.0001) x² + (2) (0.005) (x) + 28

(a) Substitute 200 and 300 to the equation,

(200) : (3) (0.0001) (200²) + (2) (0.005) (200) + 28 = 42

(300) : (3) (0.0001) (300²) + (2) (0.005) (300) + 28 = 58

The difference between the values is 16.

b. Similarly, substitute 500 to the equation,

(500) : (3) (0.0001) (500²) + (2) (0.005) (500) + 28 = 108

From a, we have 58 for 300. The difference between the values is 50.