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Calculus / Calculus: Early Transcendentals 1 / Chapter 4 / Problem 12RE

Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

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Inflection points Does f(x) = 2x 10x +20x +x+1 have any

Chapter 4, Problem 12RE

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QUESTION:

Inflection points Does \(f(x)=2 x^{5}-10 x^{4}+20 x^{3}+x+1\) have any inflection points? If so, identify them.

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QUESTION:

Inflection points Does \(f(x)=2 x^{5}-10 x^{4}+20 x^{3}+x+1\) have any inflection points? If so, identify them.

ANSWER:

Solution Step 1 In this problem we have to find the inflection point of f(x) = 2x 10x + 20x + x + 14 3 First let us see the definition of inflection points. Inflection Point: An inflection point is a point on a curve at which the sign of the curvature (i.e., the concavity) changes. Inflection points may be stationary points, but are not local maxima or local minima. A necessary condition for x to be an inflection point is f (x) = 0 3 For example, In the curve y = x plotted below, the point x = 0is an inflection point .

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