A ball was tossed into the air. its height, in metres, is given by h(t)= - 4.9t^2 + 6t + 11, where t is time, in seconds.

Question

Write an expression that represents the average rate of change over the interval 2<t<2 + h.

Answer 1

h(2) = -4.9(4) + 6(2) + 11 = 3.4
h(2+h)
= -4.9(2+h)^2 + 6(2+h) + 11
= -4.9(4 + 4h + h^2 + 12 + 6h + 11
= -19.6 - 19.6h - 4.9h^2 + h^2 + 6h + 23
= 3.4 - 3.9h^2 - 13.6h

average rate of change = (3.4 - 3.9h^2 - 13.6h - 3.4)/(2+h - 2)
= (-3.9h^2 - 13.6h)/h
= -3.9h - 13.6 , h ≠ 0