Exam 12: Derivatives Continued

Suppose that the total cost (in dollars) for a product is given by , where x is the number of units produced. Total cost functions always increase because producing more items costs more. What then must be true of the marginal cost function ?

(Multiple Choice)

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Question 61

Find if .

(Multiple Choice)

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Question 62

Find .

(Multiple Choice)

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Question 63

Find implicitly for

(Multiple Choice)

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Question 64

Medical research has shown that between heartbeats, the pressure in the aorta of a normal adult is a function of time in seconds and can be modeled by the equation . Use the derivative to find the rate at which the pressure is changing after 4.3 seconds. Round your answer to two decimal places.

(Multiple Choice)

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Question 65

Which of the following functions has the same derivative as the function below?

(Multiple Choice)

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Question 66

At what -value does the curve defined by have a horizontal tangent?

(Multiple Choice)

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Question 67

p is the price per unit in dollars and q is the number of units. The monthly demand function is and the supply function before taxation is . Find the tax per unit t that will maximize the tax revenue T.

(Multiple Choice)

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Question 68

Water is flowing into a barrel in the shape of a right circular cylinder at the rate of 700 in³ per minute. If the radius of the barrel is 3 in, at what rate is the depth of the water changing when the water is 10 in deep? Round your answer to two decimal places.

(Multiple Choice)

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Question 69

Find the derivative of the following function.

(Multiple Choice)

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Question 70

Suppose a 170-ft ladder is leaning against a wall. If the bottom is pulled away from the wall at a rate of 1 ft/sec, at what rate is the top of the ladder sliding down the wall when the bottom is 26 ft from the wall?

(Multiple Choice)

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Question 71

p is in dollars and q is the number of units. Find the elasticity of the demand function at , and use it to determine how a price increase will affect total revenue.

(Multiple Choice)

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Question 72

The demand function for specialty steel products are given, where p is in dollars and q is the number of units demanded. Find the point at which the demand is of unitary elasticity. Round your answer to two decimal places.

(Multiple Choice)

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Question 73

Suppose that the total cost (in dollars) for a product is given by , where x is the number of units produced. Find the marginal cost function.

(Multiple Choice)

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Question 74

Find dy/dx for the following equation: .

(Multiple Choice)

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Question 75

Suppose that air is being pumped into a spherical balloon at a rate of 12 in³/min.At what rate is the radius of the balloon increasing when the radius is 9 in?

(Multiple Choice)

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Question 76

Assume that x and y are differentiable functions of t. A point is moving along the graph of the equation At what rate is y changing when and is changing at a rate of 4 units/sec?

(Multiple Choice)

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Question 77

Suppose that a company's sales volume y (in dollars) is related to its advertising expenditures x (in dollars) according to Find the rate of change of sales volume, with respect to advertising expenditures when x = $70. Round your answer to two decimal places.

(Multiple Choice)

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Question 78

The radius of a circle is increasing at a rate of 6 ft/min. At what rate is its area changing when the radius is 7 ft?

(Multiple Choice)

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Question 79

For human beings, the surface area S of the body is related to the body's weight W according to , where k is a constant. For , find the percent rate of change of the body's surface area in terms of the percent rate of change of the body's weight.

(Multiple Choice)

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Question 80

Showing 61 - 80 of 139

Suppose that the total cost (in dollars) for a product is given by , where x is the number of units produced. Total cost functions always increase because producing more items costs more. What then must be true of the marginal cost function ?

Find if .

Find .

Find implicitly for

Medical research has shown that between heartbeats, the pressure in the aorta of a normal adult is a function of time in seconds and can be modeled by the equation . Use the derivative to find the rate at which the pressure is changing after 4.3 seconds. Round your answer to two decimal places.

Which of the following functions has the same derivative as the function below?

At what -value does the curve defined by have a horizontal tangent?

p is the price per unit in dollars and q is the number of units. The monthly demand function is and the supply function before taxation is . Find the tax per unit t that will maximize the tax revenue T.

Water is flowing into a barrel in the shape of a right circular cylinder at the rate of 700 in³ per minute. If the radius of the barrel is 3 in, at what rate is the depth of the water changing when the water is 10 in deep? Round your answer to two decimal places.

Find the derivative of the following function.

Suppose a 170-ft ladder is leaning against a wall. If the bottom is pulled away from the wall at a rate of 1 ft/sec, at what rate is the top of the ladder sliding down the wall when the bottom is 26 ft from the wall?

p is in dollars and q is the number of units. Find the elasticity of the demand function at , and use it to determine how a price increase will affect total revenue.

The demand function for specialty steel products are given, where p is in dollars and q is the number of units demanded. Find the point at which the demand is of unitary elasticity. Round your answer to two decimal places.

Suppose that the total cost (in dollars) for a product is given by , where x is the number of units produced. Find the marginal cost function.

Find dy/dx for the following equation: .

Suppose that air is being pumped into a spherical balloon at a rate of 12 in³/min.At what rate is the radius of the balloon increasing when the radius is 9 in?

Assume that x and y are differentiable functions of t. A point is moving along the graph of the equation At what rate is y changing when and is changing at a rate of 4 units/sec?

Suppose that a company's sales volume y (in dollars) is related to its advertising expenditures x (in dollars) according to Find the rate of change of sales volume, with respect to advertising expenditures when x = $70. Round your answer to two decimal places.

The radius of a circle is increasing at a rate of 6 ft/min. At what rate is its area changing when the radius is 7 ft?

For human beings, the surface area S of the body is related to the body's weight W according to , where k is a constant. For , find the percent rate of change of the body's surface area in terms of the percent rate of change of the body's weight.

Algebraic Concepts

Linear Equations and Functions

Quadratic and Other Special Functions

Matrices

Inequalities and Linear Programming

Exponential and Logarithmic Functions

Mathematics of Finance

Introduction to Probability

Further Topics in Probability; Data Description

Derivatives

Applications of Derivatives

Indefinite Integrals

Definite Integrals: Techniques of Integration

Functions of Two or More Variables

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Exam 12: Derivatives Continued

Suppose that the total cost (in dollars) for a product is given by , where x is the number of units produced. Total cost functions always increase because producing more items costs more. What then must be true of the marginal cost function ? ​

Find if . ​

Find . ​ ​

Find implicitly for

Medical research has shown that between heartbeats, the pressure in the aorta of a normal adult is a function of time in seconds and can be modeled by the equation . Use the derivative to find the rate at which the pressure is changing after 4.3 seconds. Round your answer to two decimal places.

Which of the following functions has the same derivative as the function below? ​ ​

At what -value does the curve defined by have a horizontal tangent? ​

p is the price per unit in dollars and q is the number of units. The monthly demand function is and the supply function before taxation is . Find the tax per unit t that will maximize the tax revenue T. ​

Water is flowing into a barrel in the shape of a right circular cylinder at the rate of 700 in3 per minute. If the radius of the barrel is 3 in, at what rate is the depth of the water changing when the water is 10 in deep? Round your answer to two decimal places.

Find the derivative of the following function. ​ ​

Suppose a 170-ft ladder is leaning against a wall. If the bottom is pulled away from the wall at a rate of 1 ft/sec, at what rate is the top of the ladder sliding down the wall when the bottom is 26 ft from the wall? ​

p is in dollars and q is the number of units. Find the elasticity of the demand function at , and use it to determine how a price increase will affect total revenue. ​

The demand function for specialty steel products are given, where p is in dollars and q is the number of units demanded. Find the point at which the demand is of unitary elasticity. Round your answer to two decimal places. ​ ​

Suppose that the total cost (in dollars) for a product is given by , where x is the number of units produced. Find the marginal cost function. ​

Find dy/dx for the following equation: ​ . ​

Suppose that air is being pumped into a spherical balloon at a rate of 12 in3/min.At what rate is the radius of the balloon increasing when the radius is 9 in?

Assume that x and y are differentiable functions of t. A point is moving along the graph of the equation At what rate is y changing when and is changing at a rate of 4 units/sec? ​

Suppose that a company's sales volume y (in dollars) is related to its advertising expenditures x (in dollars) according to Find the rate of change of sales volume, with respect to advertising expenditures when x = $70. Round your answer to two decimal places.

The radius of a circle is increasing at a rate of 6 ft/min. At what rate is its area changing when the radius is 7 ft? ​

For human beings, the surface area S of the body is related to the body's weight W according to , where k is a constant. For , find the percent rate of change of the body's surface area in terms of the percent rate of change of the body's weight. ​

Algebraic Concepts

Linear Equations and Functions

Quadratic and Other Special Functions

Matrices

Inequalities and Linear Programming

Exponential and Logarithmic Functions

Mathematics of Finance

Introduction to Probability

Further Topics in Probability; Data Description

Derivatives

Applications of Derivatives

Indefinite Integrals

Definite Integrals: Techniques of Integration

Functions of Two or More Variables

Filters

Suppose that the total cost (in dollars) for a product is given by , where x is the number of units produced. Total cost functions always increase because producing more items costs more. What then must be true of the marginal cost function ?

Find if .

Find .

Which of the following functions has the same derivative as the function below?

At what -value does the curve defined by have a horizontal tangent?

p is the price per unit in dollars and q is the number of units. The monthly demand function is and the supply function before taxation is . Find the tax per unit t that will maximize the tax revenue T.

Water is flowing into a barrel in the shape of a right circular cylinder at the rate of 700 in³ per minute. If the radius of the barrel is 3 in, at what rate is the depth of the water changing when the water is 10 in deep? Round your answer to two decimal places.

Find the derivative of the following function.

Suppose a 170-ft ladder is leaning against a wall. If the bottom is pulled away from the wall at a rate of 1 ft/sec, at what rate is the top of the ladder sliding down the wall when the bottom is 26 ft from the wall?

p is in dollars and q is the number of units. Find the elasticity of the demand function at , and use it to determine how a price increase will affect total revenue.

The demand function for specialty steel products are given, where p is in dollars and q is the number of units demanded. Find the point at which the demand is of unitary elasticity. Round your answer to two decimal places.

Suppose that the total cost (in dollars) for a product is given by , where x is the number of units produced. Find the marginal cost function.

Find dy/dx for the following equation: .

Suppose that air is being pumped into a spherical balloon at a rate of 12 in³/min.At what rate is the radius of the balloon increasing when the radius is 9 in?

Assume that x and y are differentiable functions of t. A point is moving along the graph of the equation At what rate is y changing when and is changing at a rate of 4 units/sec?

The radius of a circle is increasing at a rate of 6 ft/min. At what rate is its area changing when the radius is 7 ft?

For human beings, the surface area S of the body is related to the body's weight W according to , where k is a constant. For , find the percent rate of change of the body's surface area in terms of the percent rate of change of the body's weight.