For the following exercises, decide if the function continuous at the given point. If it is discontinuous, what type of discontinuity is it? 1'71 \f164. A small town in Ohio commissioned an actuarial firm to conduct a study that modeled the rate of change of the town's population. The study found that the town's population (measured in thousands of people) can be modeled by the function P (t) = %t3 + 6413 + 3000, where t is measured in years. a. Find the rate of change function P' (t) of the population function. b. Find P' (1) ,P' (2) ,P' (3) , and P' (4). Interpret what the results mean for the town. c. Find P \"(1) ,P"(2) ,P"(3) , and P \"(4) . Interpret what the results mean for the town's population. For the following exercises, use the quotient rule to derive the given equations. 205. d dx (cotx) = -csc2x@. You are the manager of an apartment complex with 50 units. When you set rent at $800/m0nth, all apartments are rented. As you increase rent by $25 /m011th, one fewer apartment is rented. Maintenance costs run $5U/month for each occupied unit. What is the rent that maximizes the total amount of profit