Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)

4th Edition

ISBN: 9780133178579

Author: Ross L. Finney

Publisher: PEARSON

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Question

Chapter 5.3, Problem 20E

To determine

To find all the point of inflection of the function

Expert Solution & Answer

Answer to Problem 20E

The inflection point is (0,0),(−3−0⋅43)(3,0⋅43)

Explanation of Solution

Given Information:

Given equation is,

Y=xx2+1

Calculation:

A point where the graph of a function has a tangent line and where the concavity changes is a point of inflection.

y1=(x2+1)(1)−x(2x)(x2+1)4=1−x2(x2+1)2y11=(x2+1)2(−2x)−(1−x2)(2(x2+1)2x)(x2+1)4=−2x3−2x−4x+4x3(x2+1)3=2x3−6x(x2+1)3y11=0,2x3−6x=0=2x(x2−3)=2x(x−3)(x=3)∴x=0,±3interval(−∞,−3) interval(−3,0) interval(0,3) interval(3,∞)y11(−2)=−0.03<0 y11(−1)=0.5>1 y11(1)=−0.5<0 y11(2)=0.03>0concave down concave up concave down concave up

Concaving changes at all three point, so they are inflection point

y(−3)≈−0.43y(0)≈0y(3)≈0.43

Put the three value of x into the original equation to find the y value of each point

Hence,

The inflection point is (0,0),(−3−0⋅43)(3,0⋅43)

Chapter 5.3, Problem 19E

Chapter 5.3, Problem 21E

Chapter 5 Solutions

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)

Ch. 5.1 - Prob. 1QR Ch. 5.1 - Prob. 2QR Ch. 5.1 - Prob. 3QR Ch. 5.1 - Prob. 4QR Ch. 5.1 - Prob. 5QR Ch. 5.1 - Prob. 6QR Ch. 5.1 - Prob. 7QR Ch. 5.1 - Prob. 8QR Ch. 5.1 - Prob. 9QR Ch. 5.1 - Prob. 10QR

Ch. 5.1 - Prob. 11QR Ch. 5.1 - Prob. 12QR Ch. 5.1 - Prob. 1E Ch. 5.1 - Prob. 2E Ch. 5.1 - Prob. 3E Ch. 5.1 - Prob. 4E Ch. 5.1 - Prob. 5E Ch. 5.1 - Prob. 6E Ch. 5.1 - Prob. 7E Ch. 5.1 - Prob. 8E Ch. 5.1 - Prob. 9E Ch. 5.1 - Prob. 10E Ch. 5.1 - Prob. 11E Ch. 5.1 - Prob. 12E Ch. 5.1 - Prob. 13E Ch. 5.1 - Prob. 14E Ch. 5.1 - Prob. 15E Ch. 5.1 - Prob. 16E Ch. 5.1 - Prob. 17E Ch. 5.1 - Prob. 18E Ch. 5.1 - Prob. 19E Ch. 5.1 - Prob. 20E Ch. 5.1 - Prob. 21E Ch. 5.1 - Prob. 22E Ch. 5.1 - Prob. 23E Ch. 5.1 - Prob. 24E Ch. 5.1 - Prob. 25E Ch. 5.1 - Prob. 26E Ch. 5.1 - Prob. 27E Ch. 5.1 - Prob. 28E Ch. 5.1 - Prob. 29E Ch. 5.1 - Prob. 30E Ch. 5.1 - Prob. 31E Ch. 5.1 - Prob. 32E Ch. 5.1 - Prob. 33E Ch. 5.1 - Prob. 34E Ch. 5.1 - Prob. 35E Ch. 5.1 - Prob. 36E Ch. 5.1 - Prob. 37E Ch. 5.1 - Prob. 38E Ch. 5.1 - Prob. 39E Ch. 5.1 - Prob. 40E Ch. 5.1 - Prob. 41E Ch. 5.1 - Prob. 42E Ch. 5.1 - Prob. 43E Ch. 5.1 - Prob. 44E Ch. 5.1 - Prob. 45E Ch. 5.1 - Prob. 46E Ch. 5.1 - Prob. 47E Ch. 5.1 - Prob. 48E Ch. 5.1 - 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