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