Explanation Given: The graph of the derivative f ′ is shown in Figure 1. Concept used: The points of inflections are the points at which the slope of the function changes from positive to negative or negative to positive. Calculation: A function increases when its derivative decreases. From Figure 1 , it is observed that at the point x = b the slope of f ′ ( x ) changes its sign from negative to positive, so the graph of the function f ( x ) decreases up to the point x = b Also at the point from x = b to x = e , the value of f ′ changes its sign from positive to negative, so the graph of the function f ( x ) increases up to the point x = e . From the above statement it is concluded that the points x = b , and x = e are the points of inflection of the function f ( x )

ACHIEVE FOR CALCULUS 1 TERM >CSI CUSTOM<

4th Edition

ISBN: 9781319411657

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 4.4, Problem 29E

To determine

To find:

The points of inflection of f and the interval for which f is concave down.

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Chapter 4.4, Problem 28E

Chapter 4.4, Problem 30E

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Chapter 4 Solutions

ACHIEVE FOR CALCULUS 1 TERM >CSI CUSTOM<

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The points of inflection of f and the interval for which f is concave down.

Solution Summary: The graph of the function f(x) is shown in Figure 1. The points of inflection are the points at which the slope of a function changes from positive to negative.

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To find: The points of inflection of f and the interval for which f is concave down.

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Chapter 4 Solutions

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The points of inflection of f and the interval for which f is concave down.