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Math
CalculusSingle Variable Calculus: Early Transcendentals, Volume I8th Edition

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Chapter 4.6, Problem 40E
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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

Solutions

Chapter
Section
Problem 1E
Problem 2E
Problem 3E
Problem 4E
Problem 5E
Problem 6E
Problem 9E
Problem 10E
Problem 13E
Problem 14E
Problem 27E
Problem 28E
Problem 29E
Problem 30E
Problem 33E
Problem 34E
Problem 35E
Problem 38E
Problem 39E
Problem 40E
BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

(a) Investigate the family of polynomials given by the equation f(x) = 2x3 + cx2 + 2x. For what values of c does the curve have maximum and minimum points?

(b) Show that the minimum and maximum points of every curve in the family lie on the curve y = x − x3. Illustrate by graphing this curve and several members of the family.

(a)

To determine

To find: The minimum and maximum points of the curve for different values of c.

Explanation

Given:

The function is f(x)=2x3+cx2+2x

Calculation:

Show the Equation as follows:

f(x)=2x3+cx2+2x (1)

Sketch the graph for the function f(x)=2x3+cx2+2x for different values of c as shown in Figure 1.

Differentiate Equation (1).

f′(x)=6x2+2cx+2 (2)

Modify Equation (2).

f′(x)=2(3x2+cx+1)=6x2+2cx+2

Apply the quadratic formula to solve above equation as follows:

x=−b±b2−4ac2a (3)

Substitute c for b, 3 for a, and 1 for c in Equation (3).

x=−c±c2−4(3)(1)2(3)=−c±c2−126

Thus, f has critical points

(b)

To determine

To show: The minimum and maximum points of the curves.

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Chapter 4.6,
Problem 39E
Chapter 4.7,
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Explain how the inverse of a matrix can be used to solve a system of n linear equations in n unknowns. Does the...

Finite Mathematics for the Managerial, Life, and Social Sciences

Precalculus or Calculus In Exercises 3-6.decide whether the problem can be solved using precalculus or whether ...

Calculus

The graph of y = f(3x) is obtained from the graph of y = f(x) by: stretching vertically by a factor of 3. compr...

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

True or False: If R is a rectangular region in the plane, then

Study Guide for Stewart's Multivariable Calculus, 8th

Differentiability In Exercises 35-38, show that: the function is differentiable by finding values 1 and 2 as de...

Multivariable Calculus

The paper referenced in the previous exercise also gave the 6-minute walk distances for 248 girls age 3 to 18 y...

Introduction To Statistics And Data Analysis

The Powerball lottery is played twice each week in 31 states, the District of Columbia, and the Virgin Islands....

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Solve each of the following equations using the root principle of equality. Round the answers to 3 decimal plac...

Mathematics For Machine Technology

Bank of Americas Consumer Spending Survey collected data on annual credit card charges in seven different categ...

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

Explain the distinction between naturalistic observation and contrived observation, and describe the situations...

Research Methods for the Behavioral Sciences (MindTap Course List)

Is it possible for a polynomial function to have no y-intercept? Explain and given an example.

College Algebra (MindTap Course List)

Describe the characteristics of a good hypothesis and identify examples of good and bad hypotheses.

Research Methods for the Behavioral Sciences (MindTap Course List)

Integration by Tables In Exercises 13 and 14, use a table of integrals with forms involving In u to find the in...

Calculus (MindTap Course List)

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