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Let f(x) = 8x – 9. Find the open intervals on which f is increasing (decreasing). Then, determine the r-coordinates of all relative maxima (minima). click here to read examples. 1. f is increasing on the intervals

Let f(x) = 8x – 9. Find the open intervals on which f is increasing (decreasing). Then, determine the r-coordinates of all relative maxima (minima). click here to read examples. 1. f is increasing on the intervals

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please answer number 1. And circle it
**Problem Statement:** Consider the function \( f(x) = 8x^3 - 9 \). Find the open intervals on which \( f \) is increasing or decreasing. Then, determine the \( x \)-coordinates of all relative maxima and minima of the function. - **Instructions:** 1. Identify the intervals where the function \( f \) is increasing. 2. Identify the intervals where the function \( f \) is decreasing. 3. Locate the \( x \)-coordinates where the relative maxima of \( f \) occur. 4. Locate the \( x \)-coordinates where the relative minima of \( f \) occur. - **Answer Format:** For the first two tasks (increasing and decreasing intervals), provide your answer as a single interval (e.g., \((0, 1)\)), a comma-separated list of intervals (e.g., \((-∞, 2), (3, 4)\)), or state "none" if there are no such intervals. For the last two tasks (maxima and minima), provide a comma-separated list of \( x \)-values, or state "none" if there are no such points. - **Hints:** Click on the link to read examples. - **Given Answers:** 1. \( f \) is increasing on the intervals: none 2. \( f \) is decreasing on the intervals: none 3. The relative maxima of \( f \) occur at \( x = \): none 4. The relative minima of \( f \) occur at \( x = \): none **Notes:** Ensure clarity and correctness when identifying and listing intervals or points. If the function has no intervals or points fitting the criteria, simply state "none."
Transcribed Image Text:**Problem Statement:** Consider the function \( f(x) = 8x^3 - 9 \). Find the open intervals on which \( f \) is increasing or decreasing. Then, determine the \( x \)-coordinates of all relative maxima and minima of the function. - **Instructions:** 1. Identify the intervals where the function \( f \) is increasing. 2. Identify the intervals where the function \( f \) is decreasing. 3. Locate the \( x \)-coordinates where the relative maxima of \( f \) occur. 4. Locate the \( x \)-coordinates where the relative minima of \( f \) occur. - **Answer Format:** For the first two tasks (increasing and decreasing intervals), provide your answer as a single interval (e.g., \((0, 1)\)), a comma-separated list of intervals (e.g., \((-∞, 2), (3, 4)\)), or state "none" if there are no such intervals. For the last two tasks (maxima and minima), provide a comma-separated list of \( x \)-values, or state "none" if there are no such points. - **Hints:** Click on the link to read examples. - **Given Answers:** 1. \( f \) is increasing on the intervals: none 2. \( f \) is decreasing on the intervals: none 3. The relative maxima of \( f \) occur at \( x = \): none 4. The relative minima of \( f \) occur at \( x = \): none **Notes:** Ensure clarity and correctness when identifying and listing intervals or points. If the function has no intervals or points fitting the criteria, simply state "none."
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