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1. The graph of f on [0, 10] is shown. Use it to answer the questions. Write NONE if necessary. Y 5 0 The absolute minimum value of f on [0, 10] is The absolute maximum value of f on [0, 10] is The critical numbers of f on (0, 10) are List all r values in (0, 10) where f has local maxima: List all r values in (0, 10) where f has local minima: 10 I

1. The graph of f on [0, 10] is shown. Use it to answer the questions. Write NONE if necessary. Y 5 0 The absolute minimum value of f on [0, 10] is The absolute maximum value of f on [0, 10] is The critical numbers of f on (0, 10) are List all r values in (0, 10) where f has local maxima: List all r values in (0, 10) where f has local minima: 10 I

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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### Graph Analysis on [0, 10] The graph of function \( f \) on the interval [0, 10] is displayed. Use the following details from the graph to answer the questions: - **Graph Description**: - **Axes**: The x-axis ranges from 0 to 10, and the y-axis ranges from 0 to 5. - The graph is a curve with a series of peaks and troughs: - It begins at the origin (0, 0) and rises to its first peak. - It descends to a trough, then rises to a second peak. - From there, it declines sharply. - **Critical Points**: - There are various critical points where the slope of the function changes dramatically. - Open and closed circles indicate whether endpoints are included in range at those particular x-values. ### Questions 1. **The absolute minimum value of \( f \) on [0, 10] is** _______. 2. **The absolute maximum value of \( f \) on [0, 10] is** _______. 3. **The critical numbers of \( f \) on (0, 10) are** _______. 4. **List all \( x \) values in (0, 10) where \( f \) has local maxima**: _______. 5. **List all \( x \) values in (0, 10) where \( f \) has local minima**: _______. ### Analysis - **Absolute Minimum/Maximum**: - Observe where the graph reaches the lowest and highest points within the interval. - **Critical Numbers**: - These are points within the interior of the interval (0, 10) where the derivative is zero or undefined, often corresponding to local maxima and minima. - **Local Maxima/Minima**: - Determine the x-values where peaks (maxima) or troughs (minima) occur on the graph. This involves looking for points where the curve changes direction from increasing to decreasing (local maxima), or from decreasing to increasing (local minima).
Transcribed Image Text:### Graph Analysis on [0, 10] The graph of function \( f \) on the interval [0, 10] is displayed. Use the following details from the graph to answer the questions: - **Graph Description**: - **Axes**: The x-axis ranges from 0 to 10, and the y-axis ranges from 0 to 5. - The graph is a curve with a series of peaks and troughs: - It begins at the origin (0, 0) and rises to its first peak. - It descends to a trough, then rises to a second peak. - From there, it declines sharply. - **Critical Points**: - There are various critical points where the slope of the function changes dramatically. - Open and closed circles indicate whether endpoints are included in range at those particular x-values. ### Questions 1. **The absolute minimum value of \( f \) on [0, 10] is** _______. 2. **The absolute maximum value of \( f \) on [0, 10] is** _______. 3. **The critical numbers of \( f \) on (0, 10) are** _______. 4. **List all \( x \) values in (0, 10) where \( f \) has local maxima**: _______. 5. **List all \( x \) values in (0, 10) where \( f \) has local minima**: _______. ### Analysis - **Absolute Minimum/Maximum**: - Observe where the graph reaches the lowest and highest points within the interval. - **Critical Numbers**: - These are points within the interior of the interval (0, 10) where the derivative is zero or undefined, often corresponding to local maxima and minima. - **Local Maxima/Minima**: - Determine the x-values where peaks (maxima) or troughs (minima) occur on the graph. This involves looking for points where the curve changes direction from increasing to decreasing (local maxima), or from decreasing to increasing (local minima).
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