Exam 4: Applications of Differentiation

The measurements of the base and altitude of a triangle are found to be 42 and 21 centimeters.The possible error in each measurement is 0.25 centimeter.Use differentials to estimate the propagated error in computing the area of the triangle.Round your answer to four decimal places.

(Multiple Choice)

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Question 101

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

(Multiple Choice)

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Question 102

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

(Multiple Choice)

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Question 103

Use the graph of the function given below to estimate the open intervals on which the function is increasing or decreasing.

(Multiple Choice)

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Question 104

Locate the absolute extrema of the given function on the closed interval .

(Multiple Choice)

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Question 105

Locate the absolute extrema of the function on the closed interval .Round your answers to four decimal places.

(Multiple Choice)

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Question 106

Determine whether the Mean Value Theorem can be applied to the function on the closed interval .If the Mean Value Theorem can be applied,find all numbers c in the open interval such that .

(Multiple Choice)

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Question 107

Find any critical numbers of the function .

(Multiple Choice)

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Question 108

Assume that the amount of money deposited in a bank is proportional to the square of the interest rate the bank pays on this money.Furthermore,the bank can reinvest this money at .Find the interest rate the bank should pay to maximize profit.(Use the simple interest formula. )

(Multiple Choice)

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Question 109

Analyze and sketch a graph of the function .

(Multiple Choice)

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Question 110

Find the points of inflection and discuss the concavity of the function on the interval .

(Multiple Choice)

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Question 111

If ,then on which interval(s)is the continuous function f(x)increasing?

(Multiple Choice)

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Question 112

Find all points of inflection on the graph of the function .

(Multiple Choice)

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Question 113

Determine the dimensions of a rectangular solid (with a square base)with maximum volume if its surface area is 121 square meters.

(Multiple Choice)

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Question 114

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

(Multiple Choice)

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Question 115

Suppose the deflection D of a beam of length L is ,where x is the distance from one end of the beam.Find the value of x that yields the maximum deflection.

(Multiple Choice)

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Question 116

The resistance R of a certain type of resistor is where R is measured in ohms and the temperature T is measured in degrees Celsius.Use a computer algebra system to find the critical number of the function.Round numerical values in your answer to the nearest whole number.

(Multiple Choice)

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Question 117

Determine the x-coordinate(s)of any relative extrema and inflection points of the function .

(Multiple Choice)

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Question 118

Find the length and width of a rectangle that has an area of 1,152 square feet and whose perimeter is a minimum.

(Multiple Choice)

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Question 119

Find all points of inflection on the graph of the function .

(Multiple Choice)

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Question 120

Showing 101 - 120 of 147

The measurements of the base and altitude of a triangle are found to be 42 and 21 centimeters.The possible error in each measurement is 0.25 centimeter.Use differentials to estimate the propagated error in computing the area of the triangle.Round your answer to four decimal places.

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

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

Use the graph of the function given below to estimate the open intervals on which the function is increasing or decreasing.

Locate the absolute extrema of the given function on the closed interval .

Locate the absolute extrema of the function on the closed interval .Round your answers to four decimal places.

Determine whether the Mean Value Theorem can be applied to the function on the closed interval .If the Mean Value Theorem can be applied,find all numbers c in the open interval such that .

Find any critical numbers of the function .

Assume that the amount of money deposited in a bank is proportional to the square of the interest rate the bank pays on this money.Furthermore,the bank can reinvest this money at .Find the interest rate the bank should pay to maximize profit.(Use the simple interest formula. )

Analyze and sketch a graph of the function .

Find the points of inflection and discuss the concavity of the function on the interval .

If ,then on which interval(s)is the continuous function f(x)increasing?

Find all points of inflection on the graph of the function .

Determine the dimensions of a rectangular solid (with a square base)with maximum volume if its surface area is 121 square meters.

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

Suppose the deflection D of a beam of length L is ,where x is the distance from one end of the beam.Find the value of x that yields the maximum deflection.

The resistance R of a certain type of resistor is where R is measured in ohms and the temperature T is measured in degrees Celsius.Use a computer algebra system to find the critical number of the function.Round numerical values in your answer to the nearest whole number.

Determine the x-coordinate(s)of any relative extrema and inflection points of the function .

Find the length and width of a rectangle that has an area of 1,152 square feet and whose perimeter is a minimum.

Find all points of inflection on the graph of the function .

Preparation for Calculus

Limits and Their Properties

Differentiation

Integration

Differential Equations

Applications of Integration

Integration Techniques, L'Hôpital's Rule, and Improper Integrals

Infinite Series

Parametric Equations, Polar Coordinates, and Vectors

Mechanical Ventilation and Sedation: Assessment, Medications, and Complications

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Exam 4: Applications of Differentiation

The measurements of the base and altitude of a triangle are found to be 42 and 21 centimeters.The possible error in each measurement is 0.25 centimeter.Use differentials to estimate the propagated error in computing the area of the triangle.Round your answer to four decimal places. ​

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

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

Use the graph of the function given below to estimate the open intervals on which the function is increasing or decreasing. ​ ​ ​

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

Locate the absolute extrema of the function on the closed interval .Round your answers to four decimal places. ​

Determine whether the Mean Value Theorem can be applied to the function on the closed interval .If the Mean Value Theorem can be applied,find all numbers c in the open interval such that . ​

Find any critical numbers of the function . ​

Assume that the amount of money deposited in a bank is proportional to the square of the interest rate the bank pays on this money.Furthermore,the bank can reinvest this money at .Find the interest rate the bank should pay to maximize profit.(Use the simple interest formula. ) ​

Analyze and sketch a graph of the function . ​

Find the points of inflection and discuss the concavity of the function on the interval . ​

If ,then on which interval(s)is the continuous function f(x)increasing? ​

Find all points of inflection on the graph of the function . ​

Determine the dimensions of a rectangular solid (with a square base)with maximum volume if its surface area is 121 square meters. ​

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

Suppose the deflection D of a beam of length L is ,where x is the distance from one end of the beam.Find the value of x that yields the maximum deflection. ​

The resistance R of a certain type of resistor is where R is measured in ohms and the temperature T is measured in degrees Celsius.Use a computer algebra system to find the critical number of the function.Round numerical values in your answer to the nearest whole number. ​

Determine the x-coordinate(s)of any relative extrema and inflection points of the function . ​

Find the length and width of a rectangle that has an area of 1,152 square feet and whose perimeter is a minimum. ​

Find all points of inflection on the graph of the function . ​

Preparation for Calculus

Limits and Their Properties

Differentiation

Integration

Differential Equations

Applications of Integration

Integration Techniques, L'Hôpital's Rule, and Improper Integrals

Infinite Series

Parametric Equations, Polar Coordinates, and Vectors

Mechanical Ventilation and Sedation: Assessment, Medications, and Complications

Filters

The measurements of the base and altitude of a triangle are found to be 42 and 21 centimeters.The possible error in each measurement is 0.25 centimeter.Use differentials to estimate the propagated error in computing the area of the triangle.Round your answer to four decimal places.

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

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

Use the graph of the function given below to estimate the open intervals on which the function is increasing or decreasing.

Locate the absolute extrema of the given function on the closed interval .

Locate the absolute extrema of the function on the closed interval .Round your answers to four decimal places.

Determine whether the Mean Value Theorem can be applied to the function on the closed interval .If the Mean Value Theorem can be applied,find all numbers c in the open interval such that .

Find any critical numbers of the function .

Assume that the amount of money deposited in a bank is proportional to the square of the interest rate the bank pays on this money.Furthermore,the bank can reinvest this money at .Find the interest rate the bank should pay to maximize profit.(Use the simple interest formula. )

Analyze and sketch a graph of the function .

Find the points of inflection and discuss the concavity of the function on the interval .

If ,then on which interval(s)is the continuous function f(x)increasing?

Find all points of inflection on the graph of the function .

Determine the dimensions of a rectangular solid (with a square base)with maximum volume if its surface area is 121 square meters.

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

Suppose the deflection D of a beam of length L is ,where x is the distance from one end of the beam.Find the value of x that yields the maximum deflection.

The resistance R of a certain type of resistor is where R is measured in ohms and the temperature T is measured in degrees Celsius.Use a computer algebra system to find the critical number of the function.Round numerical values in your answer to the nearest whole number.

Determine the x-coordinate(s)of any relative extrema and inflection points of the function .

Find the length and width of a rectangle that has an area of 1,152 square feet and whose perimeter is a minimum.

Find all points of inflection on the graph of the function .