A contagious and fatal virus has tragically struck the city ofPlagues Ville, which has been quarantined until the virus has run its course. The function P(t)=96t33t4 gives the number of people who are newly infected t days after the outbreak began.

(a)Find first and second derivatives P(t) and P(t).

(b)Solve P(t)=0, P(t)=0 and P(t)=0. Then complete the table.

(c)Use the table to describe the details of the Plagues Ville tragedy.