Suppose you are given the derivative of some function p(t) as p '(t) = t.cos(8t) (a) Find the exact critical point(s) of p(t) on the interval [0, /8]. t = (b) Determine p' '(t) . p''(t) = (c) Compute p' '(t) at the smallest and largest critical points you found in part (a). Indicate the concavity of p at each critical point. Smallest critical point t =to , p" '(to) = So concavity of p is: (---Select--- Largest critical point t =1 , p' '(t1) = Concavity of p is: (---Select--- (d) Perform the Second Derivative Test to classify the critical points in part (a) as local minimums or local maximums of p(t). Be sure to justify your choices. Smallest critical point of p is a (---Select--- because (---Select--- Largest critical point of p is a ( ---Select--- because (---Select