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10th Edition

Ron Larson

Publisher: Cengage Learning

ISBN: 9781305860919

Chapter 2, Problem 42RE

Textbook Problem

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**Finding the Slope of a Graph** In Exercises 41–44, find the slope of the graph of the function at the given point. Use the *derivative* feature of a graphing utility to confirm your results.

Expert Solution

To determine

**To calculate:** The slope of the graph of the function

**Given Information:**

The function

**Formula used:**

The equation of tangent of line is given by

Where *m* is equal to the slope of the tangent line to the graph of

The Constant Multiple Rule:

The Power Rule:

Where *n* is a real number.

**Calculation:**

Consider the function,

Rewrite as

Differentiate both sides the function with respect to *x*.

Now apply the constant multiple rule to get,

Calculus: An Applied Approach (MindTap Course List)

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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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Mathematical Excursions (MindTap Course List)

Evaluate expressions in Exercises 3756, rounding your answer to four significant digits where necessary. 169

Finite Mathematics

Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = 3x4 4x3 12x2 + 1, [2...

Single Variable Calculus: Early Transcendentals

Write the following numbers in word form.
4. 14.659

Contemporary Mathematics for Business & Consumers

True or False
Label each of the following statements as either true or false.
8. The set of all odd permutatio...

Elements Of Modern Algebra

What relationship subset, intersect, disjoint, or equivalent can be used to characterize the two shown in the V...

Elementary Geometry For College Students, 7e

Use the reciprocal identities for the following problems. If sec=2, find cos.

Trigonometry (MindTap Course List)

In Exercises 7-12, let x=3andy=2 . Evaluate each expression: x3y

Elementary Technical Mathematics

Using Newton's Method In Exercises 7-18, use Newton's Method to approximate the zero(s) of the function. Contin...

Calculus: Early Transcendental Functions (MindTap Course List)

Finding a Limit In Exercises 5-22, find the limit. limx0(3x2)4

Calculus of a Single Variable

For Exercises 35 to 38, make drawings as needed. In regular pentagon ABCD, sides AB- and BC-, along with diagon...

Elementary Geometry for College Students

FINANCING A HOME Sarah secured a bank loan of 200,000 for the purchase of a house. The mortgage is to be amorti...

Finite Mathematics for the Managerial, Life, and Social Sciences

Find for defined implicity by .

Study Guide for Stewart's Multivariable Calculus, 8th

Finding a Limit In Exercises 25-36, find the limit (if it exists). If the limit does not exist, explain why. li...

Multivariable Calculus

The critical numbers of f(x) = 3x4 = 20x3 36x2 are: a) 0, 1, 6 b) 0, 1, 6 c) 0, 1, 6 d) 0, 1, 6

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

Verifying a Solution In Exercises 510, verify that the function is a solution of the differential equation. Fun...

Calculus (MindTap Course List)

The Troubled Asset Relief Program (TARP), passed by the U.S. Congress in October 2008,provided 700 billion in a...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Define fraud and explain the safeguards that exist to prevent it.

Research Methods for the Behavioral Sciences (MindTap Course List)

Band trips A college band trip will require renting buses and trucks to transport no fewer than 100 students an...

College Algebra (MindTap Course List)

The average percent defective product of a manufacturing plant is 1.20%. On a particular day 50 pieces were rej...

Mathematics For Machine Technology

A student government organization is interested in estimating the proportion of students who favor a mandatory ...

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

Create an example of a citation for each of the following: a. A single author cited in parentheses. b. Two or m...

Research Methods for the Behavioral Sciences (MindTap Course List)

The paper referenced in the previous exercise also compared the reported heights and weights to actual measured...

Introduction To Statistics And Data Analysis

Reminder Round all answers to two decimal places unless otherwise indicated. Radioactive Iodine Iodine-131 is a...

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

In Exercises 87-90, use a trial-and-error process along with what you know about the digits used in a given bas...

Mathematics: A Practical Odyssey

Series Circuit Analogue Find the steady-state charge and the steady-state current in an LRC-series circuit when...

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

Show that log2n is (log2n) .

Discrete Mathematics With Applications

Service Contract Offer. Ward Doering Auto Sales is considering offering a special service contract that will co...

Essentials Of Statistics For Business & Economics

Tax Research. A study reported in The Accounting Review examined the separate and joint effects of two levels o...

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

For the following exercises, P is a point on the unit circle. a. Find the (exact) missing coordinate value of e...

Calculus Volume 1

For the following exercises, graph the equations and shade the area of the region between the curves. Determine...

Calculus Volume 2