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The graph of a function f (x) is shown. List the letter(s) of the point(s) at which f '(x)< 0 and f ''(x)> 0.

The graph of a function f (x) is shown. List the letter(s) of the point(s) at which f '(x)< 0 and f ''(x)> 0.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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The graph of a function f (x) is shown. List the letter(s) of the point(s) at which f '(x)< 0 and f ''(x)> 0.

This image presents a graph on an xy-coordinate plane, useful for educational purposes to explain concepts like graphs of functions, data points, and trends in mathematical contexts. ### Graph Explanation: - **Axes**: - The horizontal axis is labeled 'x.' - The vertical axis is labeled 'y.' - **Data Points**: - The graph includes five key data points labeled **A, B, C, D,** and **E**. - Each point is represented by a black dot. - **Curve**: - A smooth blue curve connects these points sequentially in the order A → B → C → D → E. - This curve illustrates the relationship or trend between these points in the context of the data provided. ### Points Description: - **Point A**: Located furthest left on the graph, contributing to an initial understanding of the curve's starting position. - **Point B**: Situated below Point A, indicating a downward movement. - **Point C**: Above and to the right of Point B, showing an upward progression. - **Point D**: To the right and slightly above Point C, suggesting a continued upward trend albeit more gradual. - **Point E**: To the right of Point D, showing a slight downward curve, indicating a peak followed by a minor decline. This diagram can be utilized to understand polynomial functions, trends in data science, and basic principles of calculus, including maxima, minima, and points of inflection.
Transcribed Image Text:This image presents a graph on an xy-coordinate plane, useful for educational purposes to explain concepts like graphs of functions, data points, and trends in mathematical contexts. ### Graph Explanation: - **Axes**: - The horizontal axis is labeled 'x.' - The vertical axis is labeled 'y.' - **Data Points**: - The graph includes five key data points labeled **A, B, C, D,** and **E**. - Each point is represented by a black dot. - **Curve**: - A smooth blue curve connects these points sequentially in the order A → B → C → D → E. - This curve illustrates the relationship or trend between these points in the context of the data provided. ### Points Description: - **Point A**: Located furthest left on the graph, contributing to an initial understanding of the curve's starting position. - **Point B**: Situated below Point A, indicating a downward movement. - **Point C**: Above and to the right of Point B, showing an upward progression. - **Point D**: To the right and slightly above Point C, suggesting a continued upward trend albeit more gradual. - **Point E**: To the right of Point D, showing a slight downward curve, indicating a peak followed by a minor decline. This diagram can be utilized to understand polynomial functions, trends in data science, and basic principles of calculus, including maxima, minima, and points of inflection.
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