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10th Edition

Ron Larson

Publisher: Cengage Learning

ISBN: 9781305860919

Chapter 2, Problem 63RE

Textbook Problem

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**Marginal Revenue** In Exercises 61–64, find the marginal revenue for selling *x* units. (The revenue is measured in dollars.)

Expert Solution

To determine

**To calculate:** The marginal revenue for producing *x* units when the revenue is

**Given Information:**

The revenue function is;

**Formula used:**

The Product rule of derivative is;

The Chain Rule of derivative is;

The Constant Multiple Rule of derivative is;

The Power Rule of derivative is;

Where *n* is a real number.

**Calculation:**

Consider the revenue function:

To find the marginal revenue differentiate the function with respect to *x*

Calculus: An Applied Approach (MindTap Course List)

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The cost C (In dollars) of...Ch. 2.5 - Credit Card Rate The average annual rate r (in...Ch. 2.6 - Checkpoint 1 Worked-out solution available at...Ch. 2.6 - Checkpoint 2 Worked-out solution available at...Ch. 2.6 - Checkpoint 3 Worked-out solution available at...Ch. 2.6 - Checkpoint 4 Worked-out solution available at...Ch. 2.6 - Checkpoint 5 Worked-out solution available at...Ch. 2.6 - Checkpoint 6 Worked-out solution available at...Ch. 2.6 - In Exercises 1-4, solve the equation. 16t2+292=0Ch. 2.6 - In Exercises 1-4, solve the equation. 16t2+88t=0Ch. 2.6 - In Exercises 1-4, solve the equation....Ch. 2.6 - In Exercises 1-4, solve the equation....Ch. 2.6 - In Exercises 5-8, find dy/dx. y=x2(2x+7)Ch. 2.6 - In Exercises 5-8, find dy/dx. y=(x2+3x)(2x25)Ch. 2.6 - In Exercises 5-8, find dy/dx. y=x22x+7Ch. 2.6 - In Exercises 5-8, find dy/dx. y=x2+3x2x25Ch. 2.6 - In Exercises 9 and 10, find the domain and range...Ch. 2.6 - In Exercises 9 and 10, find the domain and range...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises 112,...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises 112,...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises 112,...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises 112,...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises 112,...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises 112,...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises 112,...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises 112,...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises 112,...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises 112,...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises 112,...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises 112,...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises...Ch. 2.6 - Using Derivatives In Exercises 3134, find the...Ch. 2.6 - Using Derivatives In Exercises 3134, find the...Ch. 2.6 - Using Derivatives In Exercises 3134, find the...Ch. 2.6 - Using Derivatives In Exercises 3134, find the...Ch. 2.6 - Velocity and Acceleration A ball is propelled...Ch. 2.6 - Velocity and Acceleration A brick becomes...Ch. 2.6 - Velocity and Acceleration The velocity v (in feet...Ch. 2.6 - Stopping Distance A car is traveling at a rate of...Ch. 2.6 - Derivatives of Polynomial Functions Consider the...Ch. 2.6 - HOW DO YOU SEE IT? The graph shows the position,...Ch. 2.6 - Modeling Data The table shows the sales y (in...Ch. 2.6 - Finding a Pattern Develop a general rule for...Ch. 2.6 - True or False? In Exercises 43 and 44, determine...Ch. 2.6 - True or False? In Exercises 43 and 44, determine...Ch. 2.6 - Project: Cell Phone Subscribers in U.S. For a...Ch. 2.7 - Checkpoint 3 Worked-out solution available at...Ch. 2.7 - Checkpoint 3 Worked-out solution available at...Ch. 2.7 - Checkpoint 3 Worked-out solution available at...Ch. 2.7 - Checkpoint 4 Worked-out solution available at...Ch. 2.7 - Checkpoint 5 Worked-out solution available at...Ch. 2.7 - Checkpoint 4 Worked-out solution available at...Ch. 2.7 - In Exercises 1-6, solve the equation for y....Ch. 2.7 - In Exercises 1-6, solve the equation for y....Ch. 2.7 - In Exercises 1-6, solve the equation for y....Ch. 2.7 - In Exercises 1-6, solve the equation for y....Ch. 2.7 - In Exercises 1-6, solve the equation for y....Ch. 2.7 - In Exercises 1-6, solve the equation for y....Ch. 2.7 - In Exercises 7-9, evaluate the expression at the...Ch. 2.7 - In Exercises 7-9, evaluate the expression at the...Ch. 2.7 - In Exercises 7-9, evaluate the expression at the...Ch. 2.7 - Finding Derivatives In Exercises 1-12, find dy/dx...Ch. 2.7 - Finding Derivatives In Exercises 1-12, find dy/dx...Ch. 2.7 - Finding Derivatives In Exercises 1-12, find dy/dx...Ch. 2.7 - Finding Derivatives In Exercises 1-12, find dy/dx...Ch. 2.7 - Finding Derivatives In Exercises 1-12, find dy/dx...Ch. 2.7 - Finding Derivatives In Exercises 1-12, find dy/dx...Ch. 2.7 - Finding Derivatives In Exercises 1-12, find dy/dx...Ch. 2.7 - Finding Derivatives In Exercises 1-12, find dy/dx...Ch. 2.7 - Finding Derivatives In Exercises 1-12, find dy/dx...Ch. 2.7 - Finding Derivatives In Exercises 1-12, find dy/dx...Ch. 2.7 - Finding Derivatives In Exercises 1-12, find dy/dx...Ch. 2.7 - Finding Derivatives In Exercises 1-12, find dy/dx...Ch. 2.7 - Finding the Slope of a Graph Implicitly In...Ch. 2.7 - Finding the Slope of a Graph Implicitly In...Ch. 2.7 - Finding the Slope of a Graph Implicitly In...Ch. 2.7 - Finding the Slope of a Graph Implicitly In...Ch. 2.7 - Finding the Slope of a Graph Implicitly In...Ch. 2.7 - Finding the Slope of a Graph Implicitly In...Ch. 2.7 - Finding the Slope of a Graph Implicitly In...Ch. 2.7 - Finding the Slope of a Graph Implicitly In...Ch. 2.7 - Finding the Slope of a Graph Implicitly In...Ch. 2.7 - Finding the Slope of a Graph Implicitly In...Ch. 2.7 - Finding the Slope of a Graph Implicitly In...Ch. 2.7 - Finding the Slope of a Graph Implicitly In...Ch. 2.7 - Finding the Slope of a Graph Implicitly In...Ch. 2.7 - Finding the Slope of a Graph Implicitly In...Ch. 2.7 - Finding the Slope of a Graph Implicitly In...Ch. 2.7 - Finding the Slope of a Graph Implicitly In...Ch. 2.7 - Finding the Slope of a Graph Implicitly In...Ch. 2.7 - Finding the Slope of a Graph Implicitly In...Ch. 2.7 - Finding the Slope of a Graph Implicitly In...Ch. 2.7 - Finding the Slope of a Graph Implicitly In...Ch. 2.7 - Finding Derivatives Implicitly and Explicitly In...Ch. 2.7 - Finding Derivatives Implicitly and Explicitly In...Ch. 2.7 - Finding Equations of Tangent Lines In Exercises...Ch. 2.7 - Finding Equations of Tangent Lines In Exercises...Ch. 2.7 - Finding Equations of Tangent Lines In Exercises...Ch. 2.7 - Finding Equations of Tangent Lines In Exercises...Ch. 2.7 - Finding Equations of Tangent Lines In Exercises...Ch. 2.7 - Finding Equations of Tangent Lines In Exercises...Ch. 2.7 - Finding Equations of Tangent Lines In Exercises...Ch. 2.7 - Finding Equations of Tangent Lines In Exercises...Ch. 2.7 - Demand In Exercises 43-46, find the rate of change...Ch. 2.7 - Demand In Exercises 43-46, find the rate of change...Ch. 2.7 - Demand In Exercises 43-46, find the rate of change...Ch. 2.7 - Demand In Exercises 43-46, find the rate of change...Ch. 2.7 - Production Let x represent the units of labor and...Ch. 2.7 - HOW DO YOU SEE IT? The graph shows the demand...Ch. 2.7 - Health: U.S. Chickenpox Decline The numbers (in...Ch. 2.8 - Checkpoint 1 Worked-out solution available at...Ch. 2.8 - Checkpoint 2 Worked-out solution available at...Ch. 2.8 - Checkpoint 3 Worked-out solution available at...Ch. 2.8 - Checkpoint 4 Worked-out solution available at...Ch. 2.8 - In Exercises 1-6, write a formula for the given...Ch. 2.8 - In Exercises 1-6, write a formula for the given...Ch. 2.8 - In Exercises 1-6, write a formula for the given...Ch. 2.8 - In Exercises 1-6, write a formula for the given...Ch. 2.8 - In Exercises 1-6, write a formula for the given...Ch. 2.8 - In Exercises 1-6, write a formula for the given...Ch. 2.8 - In Exercises 7-10, find dy/dx by implicit...Ch. 2.8 - In Exercises 7-10, find dy/dx by implicit...Ch. 2.8 - In Exercises 7-10, find dy/dx by implicit...Ch. 2.8 - In Exercises 7-10, find dy/dx by implicit...Ch. 2.8 - Using Related Rates In Exercises 14, assume that x...Ch. 2.8 - Using Related Rates In Exercises 14, assume that x...Ch. 2.8 - Using Related Rates In Exercises 14, assume that x...Ch. 2.8 - Using Related Rates In Exercises 14, assume that x...Ch. 2.8 - Area The radius r of a circle is increasing at a...Ch. 2.8 - Volume The radius r of a sphere is increasing at a...Ch. 2.8 - Area Let A be the area of a circle of radius r...Ch. 2.8 - Volume Let V be the volume of a sphere of radius r...Ch. 2.8 - Volume A spherical balloon is inflated with gas at...Ch. 2.8 - Volume The radius r of a right circular cone is...Ch. 2.8 - Cost, Revenue, and Profit A company that...Ch. 2.8 - Cost, Revenue, and Profit A company that...Ch. 2.8 - Revenue The revenue R from selling x units of a...Ch. 2.8 - Profit The profit P from selling x units of a...Ch. 2.8 - Volume All edges of a cube are expanding at a rate...Ch. 2.8 - Surface Area All edges of a cube are expanding at...Ch. 2.8 - Boating A boat is pulled by a winch on a dock, and...Ch. 2.8 - Shadow Length A man 6 feet tall walks at a rate of...Ch. 2.8 - Air traffic Control An airplane flying at an...Ch. 2.8 - Baseball A (square) baseball diamond has sides...Ch. 2.8 - Air Traffic Control An air traffic controller...Ch. 2.8 - Advertising Costs A retail sporting goods store...Ch. 2.8 - Environment An accident at an oil drilling...Ch. 2.8 - Profit A company is increasing the production of a...Ch. 2.8 - Sales The profit for a product is increasing at a...Ch. 2.8 - HOW DO YOU SEE IT? 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Finding Rates of Change In Exercises 5154, find...Ch. 2 - Finding Rates of Change In Exercises 5154, find...Ch. 2 - Velocity The height s (in feet) at time t (in...Ch. 2 - Velocity A rock is dropped from a tower on the...Ch. 2 - Marginal Cost In Exercises 5760, find the marginal...Ch. 2 - Marginal Cost In Exercises 5760, find the marginal...Ch. 2 - Marginal Cost In Exercises 5760, find the marginal...Ch. 2 - Marginal Cost In Exercises 5760, find the marginal...Ch. 2 - Marginal Revenue In Exercises 6164, find the...Ch. 2 - Marginal Revenue In Exercises 6164, find the...Ch. 2 - Marginal Revenue In Exercises 6164, find the...Ch. 2 - Marginal Revenue In Exercises 6164, find the...Ch. 2 - Marginal Profit In Exercises 65 and 66, find the...Ch. 2 - Marginal Profit In Exercises 65 and 66, find the...Ch. 2 - Marginal Profit The profit P (in dollars) from...Ch. 2 - Population Growth The population P (in millions)...Ch. 2 - Finding Derivatives In Exercises 6990, find the...Ch. 2 - Finding Derivatives In Exercises 6990, find the...Ch. 2 - 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Finding Derivatives In Exercises 6990, find the...Ch. 2 - Finding Derivatives In Exercises 6990, find the...Ch. 2 - Physical Science The temperature T (in degrees...Ch. 2 - Forestry According to the Doyle Log Rule, the...Ch. 2 - Finding Higher-Order Derivatives In Exercises...Ch. 2 - Finding Higher-Order Derivatives In Exercises...Ch. 2 - Finding Higher-Order Derivatives In Exercises...Ch. 2 - Finding Higher-Order Derivatives In Exercises...Ch. 2 - Finding Higher-Order Derivatives In Exercises...Ch. 2 - Finding Higher-Order Derivatives In Exercises...Ch. 2 - Finding Higher-Order Derivatives In Exercises...Ch. 2 - Finding Higher-Order Derivatives In Exercises...Ch. 2 - Athletics A person dives from a 30-foot platform...Ch. 2 - Velocity and Acceleration The position function of...Ch. 2 - Finding Derivatives In Exercises 103106, use...Ch. 2 - Finding Derivatives In Exercises 103106, use...Ch. 2 - Finding Derivatives In Exercises 103106, use...Ch. 2 - Finding Derivatives In Exercises 103106, use...Ch. 2 - 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Graphs of populations of two species are shown. Use them to sketch the corresponding phase trajectory. 7.

Single Variable Calculus: Early Transcendentals

For regular octagon ABCDEFGH, a are quadrilateral ABGH and quadrilateral BCFG congruent? b are quadrilateral AB...

Elementary Geometry For College Students, 7e

3. To extend an invoice, for each line, we multiply the number of items by the _____ per item. (7-2)

Contemporary Mathematics for Business & Consumers

Evaluate each of the following expressions when x is /6. In each case, use exact values. 12cos2x

Trigonometry (MindTap Course List)

Find each product. 1.2m3n2(9.7m+6.5mn13n2))

Elementary Technical Mathematics

Assume the statement from Exercise 30 in section 2.1 that for all and in . Use this assumption and mathemati...

Elements Of Modern Algebra

Evaluating Trigonometric Functions In Exercises 17-20, sketch a right triangle corresponding to the trigonometr...

Calculus of a Single Variable

Finding a Derivative In Exercises 324. use the rules of differentiation to find the derivative of the function....

Calculus: Early Transcendental Functions (MindTap Course List)

In Exercises 1-6, the payoff matrix and strategies P and Q for the row and column players, respectively are giv...

Finite Mathematics for the Managerial, Life, and Social Sciences

Review Exercises In Review Exercises 22 to 24, M and N are the midpoints of FJ- and FH- respectively. Given: MN...

Elementary Geometry for College Students

Using a binomial series, the Maclaurin series for is:

Study Guide for Stewart's Multivariable Calculus, 8th

Finding an Indefinite Integral In Exercises 91-108, find the indefinite integral. e5x3dx

Calculus (MindTap Course List)

The quadratic approximation for at a = 1 is:

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

Finding Direction AnglesIn Exercises 3136, find the direction cosines and angles of u and show that cos2+cos2+c...

Multivariable Calculus

Explain the distinction between a hypothesis and a prediction.

Research Methods for the Behavioral Sciences (MindTap Course List)

The Bank of America trends in Consumer Mobility Report indicates that in a typical day,51% of users of mobile p...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

A bowlers scores for six games were 182, 168, 184, 190, 170, and 174. Using these data as a sample, compute the...

Statistics for Business & Economics, Revised (MindTap Course List)

Express the following decimal numbers as binary numbers. 10.5

Mathematics For Machine Technology

Fill in the blanks. The graph of an exponenetial function fx=bx always passes through the points 0,1 and ____.

College Algebra (MindTap Course List)

In Exercises 9-24, use Figure 3.1 to find the outcome of the bets in roulette, given the results listed. You be...

Mathematics: A Practical Odyssey

Explain how a time-series design minimizes most threats to internal validity from time-related variables.

Research Methods for the Behavioral Sciences (MindTap Course List)

The report Who Borrows Most? Bachelors Degree Recipients with High Levels of Student Debt (trends.collegeboard....

Introduction To Statistics And Data Analysis

Sales Experience and Sales Performance. In exercise 7 a sales manager collected the following data on x = annua...

Essentials Of Statistics For Business & Economics

Use the two frequency tables to compare the life expectancy of men and women from 20 randomly selected countrie...

Introductory Statistics

Reminder Round all answers to two decimal places unless otherwise indicated. Cleaning Contaminated Water A tank...

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

29. Customers arrive at a movie theater at the advertised movie time only to find that they have to sit through...

Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List)

Use the properties of even and odd integers that are listed in Example 4.3.3 to be exercise 21-23. Indicate whi...

Discrete Mathematics With Applications

Fill in the blanks. is the prediction method used to estimate a point on a line when the point does not lie b...

College Algebra

In Problems 1 -10 use the finite difference method and the indicated value of n to approximate the solution of ...

A First Course in Differential Equations with Modeling Applications (MindTap Course List)