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Sketch the graph of a function, f, that satisfies the following properties: • x = 2 is a vertical asymptote • lim f(x) = 3 • f'(-5) = 0 and f'(0) = 0 • f"(-5) = 0 • f"(-2) is undefined • f'(x) < 0 on (-2,0) • f'(x) > 0 on (-∞, -5) u (-2, –5)u (0,2) u (2, 0) • f"(x) > 0 on (-5,–2) u (-2,2) • f"(x) < 0 on (-0,-5) u (2, 0)

Sketch the graph of a function, f, that satisfies the following properties: • x = 2 is a vertical asymptote • lim f(x) = 3 • f'(-5) = 0 and f'(0) = 0 • f"(-5) = 0 • f"(-2) is undefined • f'(x) < 0 on (-2,0) • f'(x) > 0 on (-∞, -5) u (-2, –5)u (0,2) u (2, 0) • f"(x) > 0 on (-5,–2) u (-2,2) • f"(x) < 0 on (-0,-5) u (2, 0)

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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2. Sketch the graph of a function, f, that satisfies the following properties:
•x = 2 is a vertical asymptote
•limx→∞ f(x) = 3
•f′(−5) = 0 and f′(0) = 0
•f′′(−5) = 0
•f′′(−2) is undefined
•f′(x) < 0 on (−2,0)
•f′(x) > 0 on (−∞,−5) ∪ (−2,−5) ∪ (0,2) ∪ (2,∞)
•f′′(x) > 0 on (−5,−2) ∪ (−2,2)
•f′′(x) < 0 on (−∞,−5) ∪ (2,∞)

Sketch the graph of a function, f, that satisfies the following properties: • x = 2 is a vertical asymptote • lim f(x) = 3 • f'(-5) = 0 and f'(0) = 0 • f"(-5) = 0 f"(-2) is undefined • f'(x) < 0 on (-2,0) • f'(x) > 0 on (–∞,-5) U (-2,–5) u (0, 2) U (2, ∞0) • f"(x) > 0 on (-5, –2) U (-2,2) • f"(x) < 0 on (-∞,-5) U (2, 0)
Transcribed Image Text:Sketch the graph of a function, f, that satisfies the following properties: • x = 2 is a vertical asymptote • lim f(x) = 3 • f'(-5) = 0 and f'(0) = 0 • f"(-5) = 0 f"(-2) is undefined • f'(x) < 0 on (-2,0) • f'(x) > 0 on (–∞,-5) U (-2,–5) u (0, 2) U (2, ∞0) • f"(x) > 0 on (-5, –2) U (-2,2) • f"(x) < 0 on (-∞,-5) U (2, 0)
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