Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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![## Critical Points and Function Behavior Analysis
**Problem Statement**
Find the critical points and determine if the function is increasing or decreasing on the given intervals.
\[ f(x) = 6x^4 + 9x^3 \]
(Use symbolic notation and fractions where needed. Give your answer as a comma-separated list.)
**Critical Points Input**
\[ \text{critical points:} \]
\[ \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ \]
**Function Behavior**
- On \((-\infty, c_1)\) the function is:
- \(\bigcirc\) decreasing
- \(\bigcirc\) increasing
- On \((c_1, c_2)\) the function is:
- \(\bigcirc\) increasing
- \(\bigcirc\) decreasing](https://content.bartleby.com/qna-images/question/7369c9e1-cd27-40fa-b19e-4e793313e403/28bc5bdd-bc85-44bc-8d2e-305b5e069cf8/422xv52.png)
Transcribed Image Text:## Critical Points and Function Behavior Analysis
**Problem Statement**
Find the critical points and determine if the function is increasing or decreasing on the given intervals.
\[ f(x) = 6x^4 + 9x^3 \]
(Use symbolic notation and fractions where needed. Give your answer as a comma-separated list.)
**Critical Points Input**
\[ \text{critical points:} \]
\[ \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ \]
**Function Behavior**
- On \((-\infty, c_1)\) the function is:
- \(\bigcirc\) decreasing
- \(\bigcirc\) increasing
- On \((c_1, c_2)\) the function is:
- \(\bigcirc\) increasing
- \(\bigcirc\) decreasing
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