Womens soccer starting with the youth movement that took

Question

Question: Women's soccer starting with the youth movement that took hold in the 1970s and buoyed by the success of the u.s. National women's team in international competition in recent years, girls and women have taken to soccer in ever-growing numbers. The function

N(t) = -0.9307t³ + 74.04t² + 46.8667t + 3967              (0 ≤ t ≤ 16)

Gives the number of participants in women's soccer in year t, with t = 0 corresponding to the beginning of 1985.

A. Verify that the number of participants in women's soccer had been increasing from 1985 through 2000. Hint: use the quadratic formula.

B. Show that the number of participants in women's soccer had been increasing at an increasing rate from 1985 through 2000. Hint: show that the sign of n" is positive on the interval in question.