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)?