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.
