The cost C (in dollars) of producing x units of a product is C = 60x + 1350. For one week, management determined that the number of units produced x at the end of t hours can be modeled by x = −1.6t³ + 19t² − 0.5t − 1. The graph shows the cost C in terms of the time t.

(a) Using the graph, which is greater, the rate of change of the cost after 1 hour or the rate of change of the cost after 4 hours?

(b) Explain why the cost function is not increasing at a constant rate during the eight-hour shift.

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Cost (in dollars) 25,000 20,000 15,000 10,000 5,000 C w 1 Cost of Producing a Product 2 3 4 5 Time (in hours) + 6 + 7 w 8