Proof Consider a function f with continuous first and second derivatives at x = c. Prove that if f has a relative maximum at x = c, then the second Taylor polynomial centered at x = c also has a relative maximum at x = c.

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
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Chapter7: Eigenvalues And Eigenvectors
Section7.1: Eigenvalues And Eigenvectors
Problem 59E
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Proof Consider a function f with continuous first and
second derivatives at x = c. Prove that if f has a relative
maximum at x = c, then the second Taylor polynomial
centered at x = c also has a relative maximum at x = c.
Transcribed Image Text:Proof Consider a function f with continuous first and second derivatives at x = c. Prove that if f has a relative maximum at x = c, then the second Taylor polynomial centered at x = c also has a relative maximum at x = c.
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