Problem

(a) Investigate the family of polynomials given b…

07:44

Problem 38 Medium Difficulty

Investigate the family of curves given by the equation $ f(x) = x^4 + cx^2 + x $. Start by determining the transitional value of $ c $ at which the number of inflection points changes. Then graph several members of the family to see what shapes are possible. There is another transitional value of $ c $ at which the number of critical numbers changes. Try to discover it graphically. Then prove what you have discovered.

Answer

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Topics

Derivatives

Differentiation

Volume

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 4

Applications of Differentiation

Section 6

Graphing with Calculus and Calculators

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Problem 38

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Video Transcript

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Ryan C.

Arizona State University

Topics

Derivatives

Differentiation

Volume

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 4

Applications of Differentiation

Section 6

Graphing with Calculus and Calculators

Top Calculus 2 / BC Educators

Heather Z.

Oregon State University

Caleb E.

Baylor University

Samuel H.

University of Nottingham

Joseph L.

Boston College