Exam 3: Applications of the Derivative

​A rectangular page is to contain 144 square inches of print.The margins on each side are 1 inch.Find the dimensions of the page such that the least amount of paper is used. ​

​Locate the absolute extrema of the function on the closed interval ​

​A Norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular window (see figure).Find the dimensions of a Norman window of maximum area if the total perimeter is 22 feet.Round yours answers to two decimal places. ​

​The graph of f is shown.Graph f,f ' and f '' on the same set of coordinate axes. ​ ​ ​

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

​Sketch the graph of the function using any extrema,intercepts,symmetry,and asymptotes. ​

​Medication.The number of milligrams x of a medication in the bloodstream t hours after a dose is taken can be modeled by Find the t-value at which x is maximum.Round your answer to two decimal places. ​

​Volume.A rectangular box with a square base is to be formed from a square piece of metal with 54-inch sides.If a square piece with side x is cut from each corner of the metal and the sides are folded up to form an open box,the volume of the box is What value of x will maximize the volume of the box? ​ ​

​The measurement of the circumference of a circle is found to be 54 centimeters,with a possible error of 0.7 centimeters.Approximate the percent error in computing the area of the circle. ​

​Determine the open intervals on which the graph of is concave downward or concave upward. ​

​If the total revenue function for a blender is ,determine how many units x must be sold to provide the maximum total revenue in dollars. ​

​Analyze and sketch a graph of the function ​

​An employee of a delivery company earns $25.00 per hour driving a delivery van in an area where gasoline costs $2.60 per gallon.When the van is driven at a constant speed s (in miles per hour,with ),the van gets miles per gallon.Determine the most economical speed s for a 100-mile trip on an interstate highway. ​

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

​Analyze and sketch a graph of the function ​

​A firm has total revenue given by for x units of a product.Find the maximum revenue from sales of that product. ​

​Find the differential dy of the function ​

​Find the limit. ​ ​ ​

​The cost C (in millions of dollars)for the federal government to seize p% of a type of illegal drug as it enters the country is modeled by ,for Find the limit of C as ​

Find the dimensions of the rectangle of maximum area bounded by the x-axis and y-axis and the graph of ​