Exam 11: Applications of Derivatives

A printer has a contract to print 62,000 posters for a political candidate. He can run the posters by using any number of plates from 1 to 30 on his press. If he uses x metal plates, they will produce x copies of the poster with each impression of the press. The metal plates cost $3.00 to prepare, and it costs $15.00 per hour to run the press. If the press can make 1000 impressions per hour, how many metal plates should the printer make to minimize costs? Round your answer to the nearest count of metal plates. ​

Assume that the total daily cost, in dollars, of producing plastic rafts for swimming pools is given by where x is the number of rafts produced per day, then the average cost per raft produced id given by , for . Find the level of production that minimizes average cost. ​​

If the total revenue function for a blender is , find the maximum revenue if production is limited to at most 150 blenders. ​

Use the graph of to identify at which of the indicated points the derivative does not change sign. ​ ​

Both a function and its derivative are given. Use them to find all critical points.

Analytically determine any relative minima. Round your answer to two decimal places.

The running yard for a dog kennel must contain at least 900 square feet. If a 20-foot side of the kennel is used as part of one side of a rectangular yard with 900 square feet, what dimensions will require the least amount of fencing? Round your answer to the nearest feet. ​

Use the indicated x-values on the graph of to find the x-coordinate of any horizontal point of inflection.

The percent p of impurities that can be removed from the waste water of a manufacturing process at a cost of C dollars is given by . Find any C values within the domain of the problem at which the rate of change of p with respect to C does not exist. ​

The number of milligrams x of a medication in the bloodstream t hours after a dose is taken can be modeled by , . For what -values is increasing? Round answers to two decimal places.

Use the graph of to identify at which of the indicated points the derivative changes from positive to negative.

A function and its graph are given. Use the graph to find , if it exists, where . Confirm your results analytically.

A graph of is given. Use the graph to determine all critical values of . ​

Both a function and its derivative are given. Use them to find intervals on which the function is increasing.

Use the graph shown in the figure and identify points from A through I that satisfy the given condition. and

In this problem, and its graph are given. Use the graph of to determine where is concave down. ​

Find the absolute maximum for on the interval . ,

A function and its graph are given. Use the graph to find the horizontal asymptotes, if they exist. Confirm your results analytically. ​ ​ ​

Find any horizontal asymptotes for the given function.

A rectangular area is to be enclosed and divided into thirds. The family has $800 to spend for the fencing material. The outside fence costs $18 per running foot installed, and the dividers cost $22 per running foot installed. What are the dimensions that will maximize the area enclosed? Round your answer to two decimal places. ​​