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on’t graph. Just what are the inflection points and relative min/max?

on’t graph. Just what are the inflection points and relative min/max?

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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Don’t graph. Just what are the inflection points and relative min/max?
Consider a function \( f \) which is continuous on \((- \infty, 1)\) and \((1, \infty)\), has a vertical asymptote at \( x = 1 \), 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 \((-\infty, 1)\) - \( f'(x) < 0 \) on \((1, \infty)\) - \( f''(x) < 0 \) on \((-\infty, -1), (1, \infty)\) - \( f''(x) = 0 \) at \( x = -2 \) - \( f''(x) > 0 \) on \((-2, -1), (1, \infty)\) - \( f'(x) = 0 \) 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 at \( x = 1 \), 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 \((-\infty, 1)\) - \( f'(x) < 0 \) on \((1, \infty)\) - \( f''(x) < 0 \) on \((-\infty, -1), (1, \infty)\) - \( f''(x) = 0 \) at \( x = -2 \) - \( f''(x) > 0 \) on \((-2, -1), (1, \infty)\) - \( f'(x) = 0 \) at \( x = -2 \) Sketch the graph of \( f(x) \).
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