8х + 7 y = 8x

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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18-2:

Use the first derivative test and the second derivative test to determine where each function is increasing, decreasing, concave up, and concave down.

\[ y = \frac{8x + 7}{8x}, \, x \neq 0 \]
Transcribed Image Text:Use the first derivative test and the second derivative test to determine where each function is increasing, decreasing, concave up, and concave down. \[ y = \frac{8x + 7}{8x}, \, x \neq 0 \]
**Question: Identifying Concavity Intervals**

Select the correct choice below and, if necessary, fill in the answer box within your choice.

**1. Determine the intervals of concavity upward:**

- ◯ A. The function is concave up on ____.
  (Type your answer in interval notation. Use integers or fractions for any numbers in the expression. Simplify your answer.)

- ◯ B. The function is not concave up on any interval.

**2. Determine the intervals of concavity downward:**

- ◯ A. The function is concave down on ____.
  (Type your answer in interval notation. Use integers or fractions for any numbers in the expression. Simplify your answer.)

- ◯ B. The function is not concave down on any interval.
Transcribed Image Text:**Question: Identifying Concavity Intervals** Select the correct choice below and, if necessary, fill in the answer box within your choice. **1. Determine the intervals of concavity upward:** - ◯ A. The function is concave up on ____. (Type your answer in interval notation. Use integers or fractions for any numbers in the expression. Simplify your answer.) - ◯ B. The function is not concave up on any interval. **2. Determine the intervals of concavity downward:** - ◯ A. The function is concave down on ____. (Type your answer in interval notation. Use integers or fractions for any numbers in the expression. Simplify your answer.) - ◯ B. The function is not concave down on any interval.
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We use 1st and 2nd derivative test.

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