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CalculusCalculus: An Applied Approach (MindTap Course List)Finding Rates of Change In Exercises 3–12, find the average rate of change of the function over the given interval. Compare this rate with the instantaneous rates of change at the endpoints of the interval. f ( x ) = 3 x 4 / 3 ; [ 1 , 8 ]BuyFind*arrow_forward*

10th Edition

Ron Larson

Publisher: Cengage Learning

ISBN: 9781305860919

Chapter 2.3, Problem 7E

Textbook Problem

**Finding Rates of Change** In Exercises 3–12, find the average rate of change of the function over the given interval. Compare this rate with the instantaneous rates of change at the endpoints of the interval.

Expert Solution

To determine

**To calculate:** The average rate of change of the function

**Given Information:**

The provided function is

**Formula used:**

The power rule for differentiation states that,

The derivative of a constant times a function is,

Property of exponent:

According to average rate change formula, if

**Calculation:**

The average rate of change of the function

Now, substitute 1 for *x* in the function

And, substitute 8 for *x* in the function

Substituting these values in the above equation to get the average rate of change,

The average rate of change of the function

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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A survey given to a sample of college students contained questions about the following variables. For each vari...

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

let f(x) = x 1, g(x) = x+1, and h(x) = 2x3 1. Find the rule for each function. 18. ghgf

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

What does it mean to say that the line x=a is a vertical asymptote of the curve y=f(x)? Draw curves to illustra...

Calculus (MindTap Course List)

Sampling: Random Use a random-number table to generate a list of eight random number from 1 to 976. Explain you...

Understanding Basic Statistics

8. 2 and age 4 compared to children who drank whole or 2% milk (Scharf, Demmer, and DeBoer, 2013). Is this an e...

Statistics for The Behavioral Sciences (MindTap Course List)

Find the limit. 31. limr9r(r9)4

Single Variable Calculus

For Problems 51-78, simplify each of the numerical expressions. Objective 3 3[4(6+7)]+2[3(42)]

Intermediate Algebra

Find the following products.

Mathematical Applications for the Management, Life, and Social Sciences

Refer to Exercise 46. Suppose the distribution is normal (the cited article makes that assumption and even incl...

Probability and Statistics for Engineering and the Sciences

Simplify each expression in Exercises 1730, expressing your answer in positive exponent form. x2yz2(xyz1)1

Finite Mathematics

In Exercises 37 to 48, use set-builder notation to write each of the following sets. {Iowa, Ohio, Utah}

Mathematical Excursions (MindTap Course List)

Experiments show that if the chemical reaction N2O2NO2+12O2 takes place at 45C, the rate of reaction of dinitro...

Single Variable Calculus: Early Transcendentals

5. In Example 3 of Section 3.1, find elements and of such that .
From Example 3 of section 3.1: and is a set...

Elements Of Modern Algebra

Add the following fractions and reduce to lowest terms. 34+78+516

Contemporary Mathematics for Business & Consumers

In Exercises 11 to 14, determine whether the sets have a subset relationship. Are the two sets disjoint or equi...

Elementary Geometry For College Students, 7e

In Exercises 33-42, let x=1,y=2,andz=3 . Evaluate each expression: (3x4z)(2x+3z)

Elementary Technical Mathematics

Eliminate the parameter t but do not graph. x=4cott,y=4csct

Trigonometry (MindTap Course List)

Finding the Distance Between Two Points in Space In Exercises 7 and 8, find the distance between the points. (1...

Calculus: Early Transcendental Functions (MindTap Course List)

Evaluating an Improper Integral In Exercises 3348, determine whether the improper integral diverges or converge...

Calculus of a Single Variable

In Exercises 1 to 6, simplify by combining similar terms. 2(x+1)+3(x+2) HINT: Multiply before adding.

Elementary Geometry for College Students

Suppose you are given the following linear programming problem: Maximize P=ax+by, where a0 and b0, on the feasi...

Finite Mathematics for the Managerial, Life, and Social Sciences

0
2
−2
does not exist

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

Sketching a Vector Field In Exercises 914, find F and sketch several representative vectors in the vector fie...

Calculus (MindTap Course List)

Finding Minimum Distance In Exercises 19-28, use Lagrange multipliers to find the minimum distance from the cur...

Multivariable Calculus

For a = ⟨6, 2, 3⟩, b = ⟨4, 7, 9⟩, and c = ⟨8, 1, 5⟩, c · (a × b) =

Study Guide for Stewart's Multivariable Calculus, 8th

The report described in the previous exercise also classified students according to region of residence and whe...

Introduction To Statistics And Data Analysis

Describe what it means to say that science is empirical, public, and objective, and explain why each of these p...

Research Methods for the Behavioral Sciences (MindTap Course List)

A hole has a diameter of 1.6214 in.( 0.0007 in. Determine the maximum andminimum diameter.

Mathematics For Machine Technology

Forecasting Lost Sales The Carlson Department Store suffered heavy damage when a hurricane struck on August 31....

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

Exercises Solve each equation for x. 2ex=16

College Algebra (MindTap Course List)

Suppose on average a male shaver in Year 1 bought one razor handle and used 17 razor blades in a year and that ...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Identify and explain the common threats to external validity and identify threats when they appear in a researc...

Research Methods for the Behavioral Sciences (MindTap Course List)

In Problems 110 use the improved Eulers method to obtain a four-decimal approximation of the indicated value. F...

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

Round all answers to two decimal places. InflationDuring a certain period, the price of a bag of groceries grow...

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

35. To better understand how husbands and wives feel about their finances, Money Magazine conducted a national ...

Essentials Of Statistics For Business & Economics

Case Problem Lawsuit Defense Strategy
John Campbell, an employee of Manhattan Construction Company, claims to h...

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

In Exercises 39-41, use the following information: Huntingtons disease is caused by a dominant gene. One parent...

Mathematics: A Practical Odyssey

Prove the statements in 1-11. In each case use only the definitions of the terms and Assumptions listed on page...

Discrete Mathematics With Applications

Q and R are independent events. P(Q) = 0.4 and P(Q AND R) = 0.1. Find P(R).

Introductory Statistics

In the following exercises, find each indefinite integral by using appropriate substitutions. 333. cosxxsinxxco...

Calculus Volume 2