Exam 4: Applications of the Derivative

An efficiency study conducted for a company showed that the number of devices assembled by the average worker t hr after starting work at 7 A.M. is given by ​ ​ At what time during the morning shift is the average worker performing at peak efficiency? ​

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

The demand for motorcycle tires imported by Dixie Import-Export is 60,000/year and may be assumed to be uniform throughout the year. The cost of ordering a shipment of tires is $600, and the cost of storing each tire for a year is $2. ​ Determine how many tires should be in each shipment if the ordering and storage costs are to be minimized. (Assume that each shipment arrives just as the previous one has been sold.) ​ __________ tires

Using the curve-sketching guide, select the graph of the function. ​ ​

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

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

What are the dimensions of a closed rectangular box that has a square cross section, a capacity of 127 in.³ and is constructed using the least amount of material? ​

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

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 72 in.² (see the figure). ​ ​ Determine the page dimensions that will result in the maximum printed area on the page, where . ​

Using the curve-sketching guide, select the graph of the function. ​ ​

Determine where the function is concave upward. ​ ​

Determine where the function is concave upward. ​ ​

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

A stone is thrown straight up from the roof of an 90-ft building. The height (in feet) of the stone at any time (in seconds), measured from the ground, is given by . ​ What is the maximum height the stone reaches? ​ __________ ft

Show that the function has no relative extrema on . ​

Find the interval(s) where the function is increasing and the interval(s) where it is decreasing. ​ ​

The demand for motorcycle tires imported by Dixie Import-Export is 20,000/year and may be assumed to be uniform throughout the year. The cost of ordering a shipment of tires is $200, and the cost of storing each tire for a year is $2. ​ Determine how many tires should be in each shipment if the ordering and storage costs are to be minimized. (Assume that each shipment arrives just as the previous one has been sold.) ​

Find the relative maxima and relative minima, if any, of the function. Otherwise, answer none. ​ ​ Relative maxima: __________ ​ Relative minima: __________

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 $.20 for each container of cookies. The cost of storing each container of cookies over the year is $.80. ​ 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? ​

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