Explanation Given information: The statement “A function f can have 2 critical points and 3 inflection points” Applying Rolle's Theorem to f': if f ′ ( a ) = f ′ ( b ) = 0 , then there exists p in ( a , b ) such that f ′ ′ ( p ) = 0 . So there is at least one inflection point between any two critical points. Next, suppose that f has degree n . Then f ′ ′ has degree n − 2 , so it has up to n − 2 real zeros and hence up to n − 2 inflection points. It is possible for all of these to lie between adjacent critical points of f . So there is no overall maximum: there can be as many inflection points as you like between two adjacent critical points. An example with n = 5 : take

6th Edition

ISBN: 9781119399353

Author: DA

Publisher: JOHN WILEY+SONS,INC.-CONSIGNMENT

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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 17SYU

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Whether the statement is true or false.

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Chapter 4, Problem 16SYU

Chapter 4, Problem 18SYU

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Chapter 4 Solutions

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To indicate: Whether the statement is true or false.

Solution Summary: The author explains that the statement "A function f can have 2 critical points and 3 inflection points" is true or false.