Explanation Given: The redrawn graph of the derivative f ′ is shown in Figure 1. Concept used: Second Derivative Test The curve of a function is concave downward when f ″ < 0 . Calculation: From Figure 1, it is observed that in the intervals [ 0 , a ) and ( d , f ) the curve lies below the x -axis or f ″ < 0 . So, the function f ( x ) is concave downward in the interval [ 0 , a ) ∪ ( d , f ) . From Figure 1 it is observed that the point x = a acts as a transition point at which the concavity changes from concave downward to concave upward

4th Edition

ISBN: 9781319055905

Author: FRANZOSA

Publisher: VST

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Concept explainers

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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Question

Chapter 4.4, Problem 30E

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 29E

Chapter 4.4, Problem 31E

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Chapter 4 Solutions

EBK CALCULUS: EARLY TRANSCENDENTALS

Ch. 4.1 - Prob. 1PQ Ch. 4.1 - Prob. 2PQ Ch. 4.1 - Prob. 3PQ Ch. 4.1 - Prob. 4PQ Ch. 4.1 - Prob. 1E Ch. 4.1 - Prob. 2E Ch. 4.1 - Prob. 3E Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E Ch. 4.1 - Prob. 6E

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

Solution Summary: The author describes the points of inflection of f and the interval for which it is concave down.

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