Considering the following graph of the given function f. y Use the graph of f to complete the following table. f(x) f'(x) x > 0 f(x) > 0 f'(x) ? v0 x > 0 f(x) < 0 f'(x) ? v0 X < 0 f(x) > 0 f'(x) ? v0 x < 0 f(x) < 0 f'(x) ? v0

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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**Transcription for Educational Website:**

---

Considering the following graph of the given function \( f \).

![Graph of a function](#)

The graph illustrates a continuous function \( f \) that resembles a parabola opening upwards. It intersects the x-axis at two points, indicating roots on the positive \( x \)-axis, creating a symmetrical shape.

**Instructions:**

Use the graph of \( f \) to complete the following table:

| \( x \)  | \( f(x) \)     | \( f'(x) \)      |
|----------|----------------|------------------|
| \( x > 0 \) | \( f(x) > 0 \) | \( f'(x) \) ? 0 |
| \( x > 0 \) | \( f(x) < 0 \) | \( f'(x) \) ? 0 |
| \( x < 0 \) | \( f(x) > 0 \) | \( f'(x) \) ? 0 |
| \( x < 0 \) | \( f(x) < 0 \) | \( f'(x) \) ? 0 |

**Guidance for Filling the Table:**

- **Range Analysis:** Examine specific intervals of \( x \) to determine whether the function \( f \) is increasing or decreasing.
- **Derivative Sign:** Use the graph's slope in each interval to deduce if the derivative \( f'(x) \) is positive, negative, or zero.

This activity involves determining the behavior of the function and its derivative at specified intervals based on the graph.

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Transcribed Image Text:**Transcription for Educational Website:** --- Considering the following graph of the given function \( f \). ![Graph of a function](#) The graph illustrates a continuous function \( f \) that resembles a parabola opening upwards. It intersects the x-axis at two points, indicating roots on the positive \( x \)-axis, creating a symmetrical shape. **Instructions:** Use the graph of \( f \) to complete the following table: | \( x \) | \( f(x) \) | \( f'(x) \) | |----------|----------------|------------------| | \( x > 0 \) | \( f(x) > 0 \) | \( f'(x) \) ? 0 | | \( x > 0 \) | \( f(x) < 0 \) | \( f'(x) \) ? 0 | | \( x < 0 \) | \( f(x) > 0 \) | \( f'(x) \) ? 0 | | \( x < 0 \) | \( f(x) < 0 \) | \( f'(x) \) ? 0 | **Guidance for Filling the Table:** - **Range Analysis:** Examine specific intervals of \( x \) to determine whether the function \( f \) is increasing or decreasing. - **Derivative Sign:** Use the graph's slope in each interval to deduce if the derivative \( f'(x) \) is positive, negative, or zero. This activity involves determining the behavior of the function and its derivative at specified intervals based on the graph. ---
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