For the years from 2002 and projected to 2024, the U.S. per capita out-of-pocket cost for health

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For the years from 2002 and projected to 2024, the U.S. per capita out-of-pocket cost for health care C (in dollars) can be modeled by
the function

C(t) = 0.908t3 - 25.3t2 + 549t + 4540

where t is the number of years past 2000.

(a) When does the rate of change of health care costs per capita reach its minimum?

(b) On a graph of C(t), what feature occurs at the t-value found in part (a)?

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