Exam 3: Applications of Differentiation

The manager of a -unit apartment complex knows from experience that all units will be occupied if the rent is per month. A market survey suggests that, on the average, one additional unit will remain vacant for each increase in rent. What rent should the manager charge to maximize revenue?

Find the critical number(s), if any of the function

Sketch the graph of on and find its absolute maximum and absolute minimum values, if any.

Consider the following problem: A farmer with ft of fencing wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle. What is the largest possible total area of the four pens?

An aircraft manufacturer wants to determine the best selling price for a new airplane. The company estimates that the initial cost of designing the airplane and setting up the factories in which to build it will be million dollars. The additional cost of manufacturing each plane can be modeled by the function where x is the number of aircraft produced and m is the manufacturing cost, in millions of dollars. The company estimates that if it charges a price p (in millions of dollars) for each plane, it will be able to sell . Find the cost function.

Find the limit.

The owner of a ranch has 4000 yd of fencing with which to enclose a rectangular piece of grazing land situated along a straight portion of a river. If fencing is not required along the river, what are the dimensions of the largest area he can enclose? What is the area?

Find the absolute maximum and absolute minimum values, if any, of the function on [0, 25]

A fence ft tall runs parallel to a tall building at a distance of ft from the building. What is the length of the shortest ladder that will reach from the ground over the fence to the wall of the building? Round the result to the nearest hundredth.

Let and be polynomials. Find if the degree of is and the degree of is .

Sketch the graph of the function using the curve-sketching guidelines.

Find the limit.

A city's population (in thousands) t years from now is estimated by What will the population of the city be in the long run? Hint: Find