Exam 3: Applications of the Derivative

​Suppose the resident population P(in millions)of the United States can be modeled by , ,where corresponds to 1800.Analytically find the minimum and maximum populations in the U.S.for ​

​Find the x-value at which the given function has a point of inflection. ​ ​ ​

Identify the open intervals where the function is increasing or decreasing. ​

Identify the open intervals where the function is increasing or decreasing. ​

​Find all relative extrema of the function Use the Second-Derivative Test when applicable. ​

​A firm can produce 100 units per week.If its total cost function is dollars,and its total revenue function is dollars,how many units x should it produce to maximize its profit? ​

​A travel agency will plan a tour for groups of size 53 or larger.If the group contains exactly 53 people,the price is $800 per person.However,each person's price is reduced by $10 for each additional person above the 53.If the travel agency incurs a price of $150 per person for the tour,what size group will give the agency the maximum profit?

​Find all relative extrema of the function Use the Second Derivative Test where applicable. ​

​Find all relative maxima of the given function. ​ ​ ​

​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 maximum value of x.Round your answer to two decimal places. ​

​Find any critical numbers of the function ​. ​

​For the given function,find the critical numbers. ​ ​ ​

​Find all relative extrema of the function Use the Second Derivative Test where applicable. ​ ​

Find the x-value at which the absolute minimum of f(x)occurs on the interval [a,b]. ​ ​ ​

​Find the absolute extrema of the function on the closed interval Round your answer to two decimal places. ​

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

​Sketch the graph of the function given below.Choose a scale that allows all relative extrema and points of inflection to be identified on the graph. ​

Analytically determine the location(s)of any vertical asymptote(s). ​ ​ ​

Minimum cost.From a tract of land,a developer plans to fence a rectangular region and then divide it into two identical rectangular lots by putting a fence down the middle.Suppose that the fence for the outside boundary costs $7 per foot and the fence for the middle costs $4 per foot.If each lot contains 5000 square feet,find the dimensions of each lot that yield the minimum cost for the fence. ​

​Find the limit. ​ ​ ​