Explanation Concept used: A function f ( x ) has its inflection points for f ′ ′ ( x ) = 0 . Proof: Consider a cubic function of the form f ( x ) = a x 3 + b x 2 + c x + d , where a ≠ 0 and a , b , c , d are constants. As f ( x ) is a cubic polynomial in x it is always continuous and differentiable Now differentiable f ( x ) with respect to x two times f ′ ′ ( x ) =

14th Edition

ISBN: 9781464151088

Author: Associate Professor Laura Taalman, Peter Kohn

Publisher: W.H. Freeman & Company

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Chapter 3.3, Problem 94P

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To prove:that every cubic function has exactly one inflection point.

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Chapter 3.3, Problem 93P

Chapter 3.3, Problem 95P

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To prove: that every cubic function has exactly one inflection point.

Solution Summary: The author proves that every cubic function has exactly one inflection point.

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To prove:that every cubic function has exactly one inflection point.

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