Question

11. The path of a small bird in flight is given by the equation, H(t) = -.0125t3+ .15t2-.02t +10, where t (seconds) is the time where the bird has been in flight, 0≤𝑡≤15and H in metres in height. A.Find the maximum height of flight of the bird.(2)B.Find the length of time the bird was less than 9 metres. (2)C.Find an approximation for the rate of change of the bird’s height between t = 5s and t= 7s

Answer 1

H(t) = -.0125t^3+ .15t^2-.02t +10
H'(t) = -.0375t^2 + .3t - .02
(A) max H is when H' = 0
(B) H(t) < 9 for t > 12.39
(C) (H(7)-H(5))/(7-5) = ___