Exam 4: Applications of the Derivative

Phillip, the proprietor of a vineyard, estimates that the first 10,000 bottles of wine produced this season will fetch a profit of $2/bottle. However, the profit from each bottle beyond 10,000 drops by $0.0002 for each additional bottle sold. Assuming at least 10,000 bottles of wine are produced and sold, what is the maximum profit? Round the answer to two decimal places. The maximum profit is $__________ What would be the price/bottle in this case? Round the answer to the nearest cent. $__________/bottle

Find the horizontal and vertical asymptotes of the graph of the function.

Answer true or false. If f is defined on a closed interval , then f has an absolute maximum value.

You are given the graph of a function f. Determine the intervals where f is concave downward.

Neilsen Cookie Company sells its assorted butter cookies in containers that have a net content of 1 lb. The estimated demand for the cookies is 1,000,000 1-lb containers. The setup cost for each production run is $250, and the manufacturing cost is $.30 for each container of cookies. The cost of storing each container of cookies over the year is $.20. Assuming uniformity of demand throughout the year and instantaneous production, how many containers of cookies should Neilsen produce per production run in order to minimize the production cost? Hint: Show that the total production cost is given by the function . Then minimize the function on the interval (0, 1,000,000).

The average speed of a vehicle on a stretch of a route between 6 A.M. At what time of the morning commute is the traffic moving at the slowest rate? What is the average speed of a vehicle at that time? time = __________ A.M. average speed = __________ mph A.M. and 10 A.M. on a typical weekday is approximated by the function , where f (t) is measured in miles per hour and t is measured in hours, with t = 0 corresponding to 6

The concentration (in milligrams/cubic centimeter) of a certain drug in a patient's body t hr after injection is given by . When is the concentration of the drug increasing, and when is it decreasing?

Find the relative maxima and relative minima, if any, of the function.

Find the absolute maximum value and the absolute minimum value, if any, of the given function.

Find the inflection points of the following function.

Show that the function has no relative extrema on .

Find the relative maxima and relative minima, if any, of the function.

Find the relative maxima and relative minima, if any, of the function.

Find the absolute maximum value and the absolute minimum value, if any, of the given function.

The height (in feet) attained by a rocket t sec into flight is given by the function . When is the rocket rising and when is it descending?

Find the inflection points, if any, of the following function. Otherwise, answer no solution.

The owner of the Rancho Los Feliz has 2,600 yd of fencing material with which to enclose a rectangular piece of grazing land along the straight portion of a river. If fencing is not required along the river, what are the dimensions of the largest area that he can enclose? What is this area?

Sketch the graph of the function having the given properties. , , , , on , on , inflection point at

Find the inflection points, if any, of the function. Otherwise, answer no solution.

The owner of the Rancho Los Feliz has 3,000 yd of fencing material with which to enclose a rectangular piece of grazing land along the straight portion of a river. If fencing is not required along the river, what are the dimensions of the largest area that he can enclose? What is this area? __________