3. Suppose a bird takes off from the top of a lamp post with itsaltitude (in m) given by
p(t) = (1/3)t3 - (1/2)t2 -6t +15
(a) Calculate the bird’s velocity and acceleration.
(b) How tall is the lamp post?
(c) Is the bird initially flying up or down as it leaves thelamp post? Justify your answer using concepts from calculus.
(d) Determine the critical points for p(t).
(e) Determine the possible points of inflection for p(t).
(f) Determine the intervals on which p(t) is concave up andconcave down.
