A when does the rate of change of health care costs per

Question

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)?