Exam 3: Applications of the Derivative

A fast-food restaurant determines the cost model, and revenue model, for where x is the number of hamburgers sold.Determine the intervals on which the profit function is increasing and on which it is decreasing.

(Multiple Choice)

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Question 101

Find any horizontal asymptotes for the given function.

(Multiple Choice)

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Question 102

Find the open intervals on which the function is increasing or decreasing.

(Multiple Choice)

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Question 103

The profit P (in thousands of dollars)for a company spending an amount s (in thousands of dollars)on advertising is The point of diminishing returns is the point at which the rate of growth of the profit function begins to decline.Find the point of diminishing returns.Round your answer to the nearest thousand dollars.

(Multiple Choice)

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Question 104

Find the differential dy of the function

(Multiple Choice)

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Question 105

Compare dy and Δy for at x = -1 with Δx = dx = 0.01.Give your answers to four decimal places.

(Multiple Choice)

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Question 106

Use analytic methods to find the limit as for the given function.

(Multiple Choice)

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Question 107

Compare dy and Δy for at x = 1 with Δx = dx = -0.09.Give your answers to four decimal places.

(Multiple Choice)

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Question 108

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

(Multiple Choice)

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Question 109

This problem contains a function and its graph,where Use the graph to determine,as well as you can,the vertical asymptote.Check your conclusion by using the function to determine the vertical asymptote analytically.

(Multiple Choice)

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Question 110

If the total cost function for a product is dollars.Find the minimum average cost.

(Multiple Choice)

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Question 111

Find any vertical asymptotes for the given function.

(Multiple Choice)

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Question 112

Analytically determine the location of any horizontal asymptotes.

(Multiple Choice)

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Question 113

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

(Multiple Choice)

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Question 114

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

(Multiple Choice)

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Question 115

Find the open intervals on which the function is increasing or decreasing.

(Multiple Choice)

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Question 116

Use a table utility with x-values larger than 10,000 to investigate What does the table indicate about ?

(Multiple Choice)

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Question 117

Match the function with one of the following graphs.

(Multiple Choice)

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Question 118

A rancher has 440 feet of fencing to enclose two adjacent rectangular corrals (see figure).What dimensions should be used so that the enclosed area will be a maximum?

(Multiple Choice)

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Question 119

For the given function,find the relative minima.

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Question 120

A fast-food restaurant determines the cost model, and revenue model, for where x is the number of hamburgers sold.Determine the intervals on which the profit function is increasing and on which it is decreasing.

Find any horizontal asymptotes for the given function.

Find the open intervals on which the function is increasing or decreasing.

Find the differential dy of the function

Compare dy and Δy for at x = -1 with Δx = dx = 0.01.Give your answers to four decimal places.

Use analytic methods to find the limit as for the given function.

Compare dy and Δy for at x = 1 with Δx = dx = -0.09.Give your answers to four decimal places.

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

This problem contains a function and its graph,where Use the graph to determine,as well as you can,the vertical asymptote.Check your conclusion by using the function to determine the vertical asymptote analytically.

If the total cost function for a product is dollars.Find the minimum average cost.

Find any vertical asymptotes for the given function.

Analytically determine the location of any horizontal asymptotes.

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

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

Find the open intervals on which the function is increasing or decreasing.

Use a table utility with x-values larger than 10,000 to investigate What does the table indicate about ?

Match the function with one of the following graphs.

A rancher has 440 feet of fencing to enclose two adjacent rectangular corrals (see figure).What dimensions should be used so that the enclosed area will be a maximum?

For the given function,find the relative minima.

Functions, graphs, and Limits

Differentiation

Exponential and Logarithmic Functions

Integration and Its Applications

Techniques of Integration

Functions of Several Variables

Trigonometric Functions

Probability and Calculus

Series and Taylor Polynomials

Differential Equations

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Exam 3: Applications of the Derivative

​A fast-food restaurant determines the cost model, and revenue model, for where x is the number of hamburgers sold.Determine the intervals on which the profit function is increasing and on which it is decreasing. ​ ​

​Find any horizontal asymptotes for the given function. ​ ​ ​

​Find the open intervals on which the function is increasing or decreasing. ​

​Find the differential dy of the function ​

​Compare dy and Δy for at ​x​ = -1 with Δ​x​ = dx = 0.01.Give your answers to four decimal places. ​

​Use analytic methods to find the limit as for the given function. ​ ​ ​

​Compare dy and Δy for at ​x​ = 1 with Δ​x​ = dx = -0.09.Give your answers to four decimal places. ​

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

​This problem contains a function and its graph,where Use the graph to determine,as well as you can,the vertical asymptote.Check your conclusion by using the function to determine the vertical asymptote analytically. ​ ​ ​ ​ ​

​If the total cost function for a product is dollars.Find the minimum average cost. ​

​Find any vertical asymptotes for the given function. ​ ​ ​

​Analytically determine the location of any horizontal asymptotes. ​ ​ ​

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

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

​Find the open intervals on which the function is increasing or decreasing. ​

​Use a table utility with x-values larger than 10,000 to investigate What does the table indicate about ? ​

​Match the function with one of the following graphs. ​

​A rancher has 440 feet of fencing to enclose two adjacent rectangular corrals (see figure).What dimensions should be used so that the enclosed area will be a maximum? ​ ​ ​

​For the given function,find the relative minima. ​ ​ ​

Functions, graphs, and Limits

Differentiation

Exponential and Logarithmic Functions

Integration and Its Applications

Techniques of Integration

Functions of Several Variables

Trigonometric Functions

Probability and Calculus

Series and Taylor Polynomials

Differential Equations

Filters

A fast-food restaurant determines the cost model, and revenue model, for where x is the number of hamburgers sold.Determine the intervals on which the profit function is increasing and on which it is decreasing.

Find any horizontal asymptotes for the given function.

Find the open intervals on which the function is increasing or decreasing.

Find the differential dy of the function

Compare dy and Δy for at x = -1 with Δx = dx = 0.01.Give your answers to four decimal places.

Use analytic methods to find the limit as for the given function.

Compare dy and Δy for at x = 1 with Δx = dx = -0.09.Give your answers to four decimal places.

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

This problem contains a function and its graph,where Use the graph to determine,as well as you can,the vertical asymptote.Check your conclusion by using the function to determine the vertical asymptote analytically.

If the total cost function for a product is dollars.Find the minimum average cost.

Find any vertical asymptotes for the given function.

Analytically determine the location of any horizontal asymptotes.

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

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

Find the open intervals on which the function is increasing or decreasing.

Use a table utility with x-values larger than 10,000 to investigate What does the table indicate about ?

Match the function with one of the following graphs.

A rancher has 440 feet of fencing to enclose two adjacent rectangular corrals (see figure).What dimensions should be used so that the enclosed area will be a maximum?

For the given function,find the relative minima.