Business Management—Production Costs: The A&D Publishing Company has determined that the printing cost of its new self-help book Me and You Too can be modeled by the cost function
C(x) = 0.02x3 − 0.6x2 + 9.15x + 98.43 0 ≤ x ≤ 40
where x represents the number of books produced each day and C(x) represents the daily production cost in thousands of dollars.
(a) Determine the differential dy = C′(x)dx for the model.
(b) Favorable reviews of the book have resulted in an increase in daily production from 19 to 20 books. Use the differential to approximate the change in production cost.
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