Explanation Given: The given statement is “Suppose f and f ′ are differentiable on an interval I . If _ is positive on I , then f is concave up on I . If _ is _ on I , then f is concave down on I .” Concept Used: Definition of concavity: Suppose f and f ′ are differentiable on an interval I . Then, If f ′ is increasing; i.e. positive on I , then f is concave up on I . If f ′ is decreasing; i.e. negative on I , then f is concave down on I

14th Edition

ISBN: 9781464151088

Author: Associate Professor Laura Taalman, Peter Kohn

Publisher: W.H. Freeman & Company

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Chapter 3, Problem 9T

To determine

To fill the blank to complete the given statement:

“Suppose f and f′ are differentiable on an interval I . If _ is positive on I , then f is concave up on I . If _ is _ on I , then f is concave down on I .”

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Chapter 3, Problem 8T

Chapter 3, Problem 10T

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Chapter 3 Solutions

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To fill the blank to complete the given statement: “Suppose f and f ′ are differentiable on an interval I . If _ is positive on I , then f is concave up on I . If _ is _ on I , then f is concave down on I .”

Solution Summary: The author explains the definition of concavity of f and fprime.

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To fill the blank to complete the given statement:

“Suppose f and f′ are differentiable on an interval I . If _ is positive on I , then f is concave up on I . If _ is _ on I , then f is concave down on I .”

Want to see the full answer?

Chapter 3 Solutions

To fill the blank to complete the given statement: “Suppose f and f ′ are differentiable on an interval I . If _ is positive on I , then f is concave up on I . If _ is _ on I , then f is concave down on I .”

Solution Summary: The author explains the definition of concavity of f and fprime.

Videos

To fill the blank to complete the given statement: “Suppose f and f′ are differentiable on an interval I . If _ is positive on I , then f is concave up on I . If _ is _ on I , then f is concave down on I .”

Want to see the full answer?

Chapter 3 Solutions

To fill the blank to complete the given statement:

“Suppose f and f′ are differentiable on an interval I . If _ is positive on I , then f is concave up on I . If _ is _ on I , then f is concave down on I .”