Single Variable Calculus: Early Transcendentals Plus MyLab Math with Pearson eText -- Access Card Package (2nd Edition) (Briggs/Cochran/Gillett Calculus 2e)

2nd Edition

ISBN: 9780321965172

Author: William L. Briggs, Lyle Cochran, Bernard Gillett

Publisher: PEARSON

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Textbook Question

Chapter 9.1, Problem 94E

Local extreme points and inflection points Suppose f has continuous first and second derivatives at a.

a. Show that if f has a local maximum at a, then the Taylor polynomial p₂ centered at a also has a local maximum at a.
b. Show that if f has a local minimum at a, then the Taylor polynomial p₂ centered at a also has a local minimum at a.
c. Is it true that if f has an inflection point at a, then the Taylor polynomial p₂ centered at a also has an inflection point at a?
d. Are the converses in parts (a) and (b) true? If p₂ has a local extreme point at a, does f have the same type of point at a?

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Chapter 9.1, Problem 93E

Chapter 9.1, Problem 95E

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Local extreme points and inflection points Suppose ƒ has continuousfirst and second derivatives at a.a. Show that if ƒ has a local maximum at a, then the Taylor polynomialp2 centered at a also has a local maximum at a.b. Show that if ƒ has a local minimum at a, then the Taylor polynomialp2 centered at a also has a local minimum at a.c. Is it true that if ƒ has an inflection point at a, then the Taylor polynomial p2 centered at a also has an inflection point at a?d. Are the converses in parts (a) and (b) true? If p2 has a local extremepoint at a, does ƒ have the same type of point at a?

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Chapter 9 Solutions

Single Variable Calculus: Early Transcendentals Plus MyLab Math with Pearson eText -- Access Card Package (2nd Edition) (Briggs/Cochran/Gillett Calculus 2e)

Ch. 9.1 - Prob. 1QC Ch. 9.1 - Prob. 2QC Ch. 9.1 - Prob. 3QC Ch. 9.1 - Prob. 4QC Ch. 9.1 - Prob. 5QC Ch. 9.1 - In Example 7, find an approximate upper bound for...Ch. 9.1 - Suppose you use a second-order Taylor polynomial...Ch. 9.1 - Does the accuracy of an approximation given by a...Ch. 9.1 - The first three Taylor polynomials for f(x)=1+x...Ch. 9.1 - Prob. 4E

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