College Algebra (MindTap Course List)
12th Edition
ISBN: 9781305652231
Author: R. David Gustafson, Jeff Hughes
Publisher: Cengage Learning
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![### Question 2
#### On which of the following intervals is \( f(x) = x^2 \cdot \sqrt[3]{x - 7} \) concave down?
- **A.** \((-∞, 3)\)
- **B.** \((4, 5)\)
- **C.** \((5, 6)\)
- **D.** \((7, 8)\)
- **E.** \((10, ∞)\)
**Note:** Moving to the next question prevents changes to this answer.](https://content.bartleby.com/qna-images/question/db00ba32-d4f4-45bb-8d8d-5bfe9040ed09/8b438612-5e99-4414-9d6a-9069e6f0d2fb/6i17lsw.jpeg)
Transcribed Image Text:### Question 2
#### On which of the following intervals is \( f(x) = x^2 \cdot \sqrt[3]{x - 7} \) concave down?
- **A.** \((-∞, 3)\)
- **B.** \((4, 5)\)
- **C.** \((5, 6)\)
- **D.** \((7, 8)\)
- **E.** \((10, ∞)\)
**Note:** Moving to the next question prevents changes to this answer.
Expert Solution
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Step 1
Given:
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Step 2
Finding f’(x):
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Step 3
Finding f''(x)
Taking the derivative again, we get:
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