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10. The following is the graph of f'(x)(the first derivative!). When A. (-4, –2) U (0, 2.5) U (4.5, ∞) В. (0),3) U (5, оо) C. (-4, 0) U (1, ∞) D. (-0, –5) U (5, ∞) E. (-∞,–5) U (1, 4) U (5, ∞) F. None of these brin 0.5 -0.5

10. The following is the graph of f'(x)(the first derivative!). When A. (-4, –2) U (0, 2.5) U (4.5, ∞) В. (0),3) U (5, оо) C. (-4, 0) U (1, ∞) D. (-0, –5) U (5, ∞) E. (-∞,–5) U (1, 4) U (5, ∞) F. None of these brin 0.5 -0.5

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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**Question 10:** The following is the graph of \( f'(x) \) (the first derivative). When is \( f(x) \) increasing? **Options:** A. \((-4, -2) \cup (0, 2.5) \cup (4.5, \infty)\) B. \((0, 3) \cup (5, \infty)\) C. \((-4, 0) \cup (1, \infty)\) D. \((-\infty, -5) \cup (5, \infty)\) E. \((-\infty, -5) \cup (1, 4) \cup (5, \infty)\) F. None of these **Graph Description:** The graph provided represents the first derivative, \( f'(x) \). It shows: - A segment decreasing below the x-axis starting from the left and crossing the x-axis near \( x = -5.5 \). It reaches a minimum at about \( x = -5 \), and then increases, crossing the x-axis at \( x = -3.5 \). - The graph remains above the x-axis indicating an increasing function for \( x \) values just above \( -3.5 \), peaking at \( x = 1 \). - It descends again between \( x = 2 \) and \( x = 3 \). - After \( x = 3 \), the graph increases and crosses the x-axis near \( x = 4 \). - A notable decrease occurs between \( x = 4 \) and \( x = 5 \) before sharply increasing past \( x = 5 \) into \(\infty\). **Conclusion:** To determine when \( f(x) \) is increasing, identify the intervals where \( f'(x) > 0\). The graph shows \( f'(x) > 0 \) approximately within the intervals \((-3.5, 1)\), \((4, 5)\), and \((5, \infty)\). These correspond most closely to option E.
Transcribed Image Text:**Question 10:** The following is the graph of \( f'(x) \) (the first derivative). When is \( f(x) \) increasing? **Options:** A. \((-4, -2) \cup (0, 2.5) \cup (4.5, \infty)\) B. \((0, 3) \cup (5, \infty)\) C. \((-4, 0) \cup (1, \infty)\) D. \((-\infty, -5) \cup (5, \infty)\) E. \((-\infty, -5) \cup (1, 4) \cup (5, \infty)\) F. None of these **Graph Description:** The graph provided represents the first derivative, \( f'(x) \). It shows: - A segment decreasing below the x-axis starting from the left and crossing the x-axis near \( x = -5.5 \). It reaches a minimum at about \( x = -5 \), and then increases, crossing the x-axis at \( x = -3.5 \). - The graph remains above the x-axis indicating an increasing function for \( x \) values just above \( -3.5 \), peaking at \( x = 1 \). - It descends again between \( x = 2 \) and \( x = 3 \). - After \( x = 3 \), the graph increases and crosses the x-axis near \( x = 4 \). - A notable decrease occurs between \( x = 4 \) and \( x = 5 \) before sharply increasing past \( x = 5 \) into \(\infty\). **Conclusion:** To determine when \( f(x) \) is increasing, identify the intervals where \( f'(x) > 0\). The graph shows \( f'(x) > 0 \) approximately within the intervals \((-3.5, 1)\), \((4, 5)\), and \((5, \infty)\). These correspond most closely to option E.
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