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Per capita health care costs
For the years from 2000 and projected to 2018, the U.S. per capita out-of-pocket cost for health care C (in dollars) can be modeled by the function
C(t) = 0.118t3 - 2.51t2 + 40.2t + 677
where t is the number of years past 2000 (Source: U.S. Centers for Medicare and Medicaid Services).
(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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