Explanation Given information: The statement “If f ' ' ( x ) = x ( x + 1 ) 2 then f has an inflection point at x = − 1 ” A point x = p is called an inflection point if the function is continuous at the point and the concavity of the graph changes at that point. If f '' > 0 on an interval, then f is concave up on that interval. If f '' < 0 on an interval, then f is concave down on that interval. If f ' ' changes sign (from positive to negative or from negative to positive) at a point x = p , then there is an inflection point located at x = p on the graph. In particular, the point ( p , f ( p ) ) is an inflection point for the function f . f ' ' ( − 1 ) = − 1 ( − 1 + 1 ) 2 = − 1 ( 0 ) 2 = 0 f ' ' ( − 1

6th Edition

ISBN: 9781119399322

Author: Hughes-Hallett

Publisher: WILEY

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

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Chapter 4, Problem 19SYU

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To indicate:

Whether the statement is true or false.

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Chapter 4, Problem 18SYU

Chapter 4, Problem 20SYU

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Chapter 4 Solutions

APPLIED CALCULUS (WILEY PLUS)

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To indicate: Whether the statement is true or false.

Solution Summary: The author explains that a point x=p is an inflection point if the function is continuous at the point and the concavity of the graph changes at that point.