Exam 4: Applications of the Derivative

The estimated monthly profit (in dollars) realizable by Cannon Precision Instruments for manufacturing and selling units of its model M1 camera is . ​ To maximize its profits, how many cameras should Cannon produce each month? ​ __________ cameras

Use the information summarized in the table to select the graph of Domain: Intercept: x-intercept: 01 Asymptotes: x-axis and y-axis Intervals where f is ↑ and ↓: ↑ on ↓ on Relative extrems: Rel. max. at Concavity: Downward on ; upward Point of inflection: ​

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

Using the curve-sketching guide, select the graph 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? ​

The management of the UNICO department store has decided to enclose an 400ft² area outside the building for displaying potted plants and flowers. One side will be formed by the external wall of the store, two sides will be constructed of pine boards, and the fourth side will be made of galvanized steel fencing material. ​ ​ If the pine board fencing costs $8/running foot and the steel fencing costs $2/running foot, determine the dimensions of the enclosure that can be erected at minimum cost.

A book designer has decided that the pages of a book should have 1 in.margins at the top and bottom and in.margins on the sides. She further stipulated that each page should have an area of 27 in.² (see the figure). ​ ​ Determine the page dimensions that will result in the maximum printed area on the page, where . ​

Find the inflection points, if any, of the function. ​ ​

If is defined on a closed interval , then has an absolute maximum value.

Phillip, the proprietor of a vineyard, estimates that the first 10,000 bottles of wine produced this season will fetch a profit of $4/bottle. However, the profit from each bottle beyond 10,000 drops by $0.0004 for each additional bottle sold. ​ Assuming at least 10,000 bottles of wine are produced and sold, what is the maximum profit? What would be the price/bottle in this case? ​

Suppose the total cost function for manufacturing a certain product is dollars, where represents the number of units produced. Find the level of production that will minimize the average cost. Round the answer to the nearest integer. ​__________ units

The figure depicts a racetrack with ends that are semicircular in shape. The length of the track is . ​ ​ Find r and lso that the area enclosed by the rectangular region of the racetrack is as large as possible. ​

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

A manufacturer of tennis rackets finds that the total cost (in dollars) of manufacturing rackets/day is given by . Each racket can be sold at a price of dollars, where is related to by the demand equation . ​ If all rackets that are manufactured can be sold, find the daily level of production that will yield a maximum profit for the manufacturer. ​

Find the horizontal and vertical asymptotes of the graph. ​ ​ Horizontal asymptote is __________ ​ Vertical asymptote is __________ ​

Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. If the graph of f is concave downward on (a, b), then the graph of - f is concave upward on (a, b).

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

A city's main well was recently found to be contaminated with trichloroethylene (a cancer-causing chemical) as a result of an abandoned chemical dump leaching chemicals into the water. A proposal submitted to the city council indicated that the cost, measured in millions of dollars, of removing x% of the toxic pollutants is given by . ​ Find the vertical asymptote of C(x). Is it possible to remove 99% of the toxic pollutant from the water? ​

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