Spread of hiv the estimated number of children newly

Question

Question: SPREAD OF HIV The estimated number of children newly infected with HIV through mother-to-child contact worldwide is given by

f(t) = -0.2083t³ + 3.0357t² + 44.0476t + 200.2857             (0 ≤ t ≤ 12)

where f(t) is measured in thousands and t is measured in years, with t = 0 corresponding to the beginning of 1990.

a. Plot the graph of f in the viewing window [0, 12] × [0, 800].

b. How fast was the estimated number of children newly infected with HIV through mother-to-child contact worldwide increasing at the beginning of the year 2000?