1. The unit price of an item affects its supply and demand. That is, if the unit price rises, demand for the item will generally decrease. A local newspaper currently has 42,000 subscribers with a quarterly charge of $40. Market research has suggested that if owners raised the price to $42, they would lose 1,000 subscribers. Assuming that subscriptions are linearly related to price, apply the maximum and minimum values relative maximum and minimum values of a polynomial functionto determine how much the periodical should charge for a quarterly subscription to maximize its income .

2. The profit of selling local ballet tickets depends on the price of the ticket. Wearing

past receipts, we find that profit can be modeled by the function p=-10x ² + 200x + 45 , where x is the price of each ticket. Apply the relative maximum and minimum values of a polynomial functionto determine the price of the ticket that provides the maximum profit and the value of the maximum profit.

3. Consider the polynomial p(x)= x ³ -7x-40 .Evaluate p(6) and p(-4) . Apply the properties of functions to predict the behavior of the function at one of the x -intercepts of p(x). .