The median income f (x), in thousands of dollars, is a function of the age of workers ages 20-62, x, and can be modeled by
f (x) = 0.000864x3 - 0.128x2 + 6.61x - 62.6
(a) Find the instantaneous rate of change of the median income function.
(b) Find the instantaneous rate of change of the median income for 25-year-old and 55-year-old workers.
(c) Find the second derivative of the median income function.
(d) Use the second derivative to determine how fast the instantaneous rate of change in the median income of workers is changing for 25-year-old and 55-year-old workers.
(e) Explain the meaning f'(55) and f"(55).