Consider the graph of a function f. y Identify the correct statements about the graph. O f'(x) > 0 for all x O f'(x) < 0 for all x f has one local minimum and one local maximum. f"(x) > 0 for x > 0 f has one inflection point. O f"(x) < 0 for x < 0

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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**Title: Analyzing the Graph of a Function \( f \)**

**Description:**

Consider the graph of a function \( f \) depicted above. The graph exhibits the following characteristics:

- The curve passes through the origin and increases without bound as \( x \) approaches positive or negative infinity.
- The slope of the tangent line (derivative) seems to be positive for most of the values of \( x \).

**Task:**

Identify the correct statements about the graph:

- [ ] \( f'(x) > 0 \) for all \( x \)
- [ ] \( f'(x) < 0 \) for all \( x \)
- [ ] \( f \) has one local minimum and one local maximum.
- [ ] \( f''(x) > 0 \) for \( x > 0 \)
- [ ] \( f \) has one inflection point.
- [ ] \( f''(x) < 0 \) for \( x < 0 \)
Transcribed Image Text:**Title: Analyzing the Graph of a Function \( f \)** **Description:** Consider the graph of a function \( f \) depicted above. The graph exhibits the following characteristics: - The curve passes through the origin and increases without bound as \( x \) approaches positive or negative infinity. - The slope of the tangent line (derivative) seems to be positive for most of the values of \( x \). **Task:** Identify the correct statements about the graph: - [ ] \( f'(x) > 0 \) for all \( x \) - [ ] \( f'(x) < 0 \) for all \( x \) - [ ] \( f \) has one local minimum and one local maximum. - [ ] \( f''(x) > 0 \) for \( x > 0 \) - [ ] \( f \) has one inflection point. - [ ] \( f''(x) < 0 \) for \( x < 0 \)
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