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The graph of f'(æ) is shown below. Where is f (x) decreasing? y =f '(x) 10

The graph of f'(æ) is shown below. Where is f (x) decreasing? y =f '(x) 10

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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**Title: Understanding Where a Function is Decreasing** **Introduction:** The graph of \( f'(x) \) is shown below. Our task is to determine where the function \( f(x) \) is decreasing. Recall that a function \( f(x) \) is decreasing on intervals where its derivative \( f'(x) \) is negative. **Graph Explanation:** - The graph depicts the function \( y = f'(x) \). - The horizontal axis is labeled \( x \), and the vertical axis represents \( y = f'(x) \). - Key points on the graph include: - \( f'(x) \) starts above the x-axis and moves downward, crossing below the x-axis at approximately \( x = -3 \). - \( f'(x) \) rises and crosses above the x-axis again at approximately \( x = 2 \). - The graph is below the x-axis between \( x = -3 \) and \( x = 2 \), indicating intervals where \( f(x) \) is decreasing. **Answer Choices:** a) \( f(x) \) is decreasing on the intervals \((-\infty, -3)\) and \((2, 8)\). b) \( f(x) \) is decreasing on the intervals \((-3, 2)\) and \((8, \infty)\). c) \( f(x) \) is decreasing on the interval \((-3, \infty)\). d) \( f(x) \) is decreasing on the interval \((-3, 8)\). e) \( f(x) \) is decreasing on the interval \((-\infty, -3)\). **Conclusion:** Identify the intervals where \( f'(x) \) is less than zero. Analyzing the graph, the function \( f(x) \) is decreasing when \( x \) is in the range \((-3, 2)\), as \( f'(x) \) is negative in this interval. The correct choice is: **b) \( f(x) \) is decreasing on the intervals \((-3, 2)\) and \((8, \infty)\).**
Transcribed Image Text:**Title: Understanding Where a Function is Decreasing** **Introduction:** The graph of \( f'(x) \) is shown below. Our task is to determine where the function \( f(x) \) is decreasing. Recall that a function \( f(x) \) is decreasing on intervals where its derivative \( f'(x) \) is negative. **Graph Explanation:** - The graph depicts the function \( y = f'(x) \). - The horizontal axis is labeled \( x \), and the vertical axis represents \( y = f'(x) \). - Key points on the graph include: - \( f'(x) \) starts above the x-axis and moves downward, crossing below the x-axis at approximately \( x = -3 \). - \( f'(x) \) rises and crosses above the x-axis again at approximately \( x = 2 \). - The graph is below the x-axis between \( x = -3 \) and \( x = 2 \), indicating intervals where \( f(x) \) is decreasing. **Answer Choices:** a) \( f(x) \) is decreasing on the intervals \((-\infty, -3)\) and \((2, 8)\). b) \( f(x) \) is decreasing on the intervals \((-3, 2)\) and \((8, \infty)\). c) \( f(x) \) is decreasing on the interval \((-3, \infty)\). d) \( f(x) \) is decreasing on the interval \((-3, 8)\). e) \( f(x) \) is decreasing on the interval \((-\infty, -3)\). **Conclusion:** Identify the intervals where \( f'(x) \) is less than zero. Analyzing the graph, the function \( f(x) \) is decreasing when \( x \) is in the range \((-3, 2)\), as \( f'(x) \) is negative in this interval. The correct choice is: **b) \( f(x) \) is decreasing on the intervals \((-3, 2)\) and \((8, \infty)\).**
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