A contagious and fatal virus has tragically struck the city of Plaguesville, which has been quarantined until the virus has run its course. The function P(t) = 48t - 1.5t* 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'(1) = 0 and P"(t) = 0. Then complete the table. (c) Use the table to describe the details of the Plaguesville tragedy (a) Find first and second derivatives P'(t) and P"(t) P' (t) = 1441 -6+ P"(t) = 288t - 181- (b) Solve P(t), P'(t), and P"(t) for 0 in order to complete the table Days P(t) P'(t) P"(t) 0 0 0 0