max the dog is chasing after some birds in the park. Max runs directly east to s

Question

max the dog is chasing after some birds in the park. Max runs directly east to scatter a pile of birds before turning directly around to scatter a second pile of birds that formed behind him. Finally max turns around again, running to east and scattering a third large pile of birds. Max's velocity (measured in m/s^2) is given by the equation v(t)=(3t^2)-21t+30 where t is the time measured in seconds since Max started running. (a) At what points in time does Max change direction from running east to west and west to east?

Explanation / Answer

v(t) = 3t2-21t+30 =3(t-5)(t-2)

so velocity will be 0 at t=5 and 2 and hence he must have changed his direction at t= 2s and t=5s

v'(t) = 6t-21

v'(t) =0 gives t = 21/6

v"(t) = 6 >0 for all t

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