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Consider a function f which is continuous on (-∞, 1) and (1, ∞), has a vertical asymptote = 1, has a horizontal asymptote y = 0, and for which the following conditions hold: f(-2) = -1, f(-1) = -2, ƒ(0) = 0, ƒ(2) = 2 f'(x) > 0 on (-1,1) f'(x) <0 on (-∞, -1), (1, ∞) f'(x) = 0 at x = -1 f"(x) > 0 on (-2, 1), (1, ∞) on (-∞, -2) f"(x) <0 on ( f"(x) = 0 at x = -2. Sketch the graph of f(x).

Consider a function f which is continuous on (-∞, 1) and (1, ∞), has a vertical asymptote = 1, has a horizontal asymptote y = 0, and for which the following conditions hold: f(-2) = -1, f(-1) = -2, ƒ(0) = 0, ƒ(2) = 2 f'(x) > 0 on (-1,1) f'(x) <0 on (-∞, -1), (1, ∞) f'(x) = 0 at x = -1 f"(x) > 0 on (-2, 1), (1, ∞) on (-∞, -2) f"(x) <0 on ( f"(x) = 0 at x = -2. Sketch the graph of f(x).

Calculus: Early Transcendentals
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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Consider a function \( f \) which is continuous on \((- \infty , 1)\) and \((1, \infty)\), has a vertical asymptote \( x = 1 \), has a horizontal asymptote \( y = 0 \), and for which the following conditions hold: \( f(-2) = -1, f(-1) = -2, f(0) = 0, f(2) = 2 \) \( f'(x) > 0 \) on \((-1, 1)\) \( f'(x) < 0 \) on \((-\infty, -1), (1, \infty)\) \( f'(x) = 0 \) at \( x = -1 \) \( f''(x) > 0 \) on \((-2, 1), (1, \infty)\) \( f''(x) < 0 \) on \((-\infty, -2), (2, \infty)\) \( f''(x) = 0 \) at \( x = -2 \). Sketch the graph of \( f(x) \).
Transcribed Image Text:Consider a function \( f \) which is continuous on \((- \infty , 1)\) and \((1, \infty)\), has a vertical asymptote \( x = 1 \), has a horizontal asymptote \( y = 0 \), and for which the following conditions hold: \( f(-2) = -1, f(-1) = -2, f(0) = 0, f(2) = 2 \) \( f'(x) > 0 \) on \((-1, 1)\) \( f'(x) < 0 \) on \((-\infty, -1), (1, \infty)\) \( f'(x) = 0 \) at \( x = -1 \) \( f''(x) > 0 \) on \((-2, 1), (1, \infty)\) \( f''(x) < 0 \) on \((-\infty, -2), (2, \infty)\) \( f''(x) = 0 \) at \( x = -2 \). Sketch the graph of \( f(x) \).
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