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lim f(x) = -∞ x-2- lim, f(x) = 0 x--2+ lim f(x) =-3+ %3D X00 f(-7) = 3 f'(-4) = 0 f(-6) = 0 f'(-1) = 0 f(-4) = -2 f'(1) DNE f(-1) = 0 f"(-6) = 0 f(1) = 3 f"(-4) = 0 f(2) = 0 f'(x) > 0 on x E (-1,1) f'(x) < 0 on x E (-, –2) U (–2, -1) U (1, 0) f"(x) > 0 on x E (-6, –4) U (–2, ∞) f"(x) < 0 on x E (-0, –6) U (-4, –2)

lim f(x) = -∞ x-2- lim, f(x) = 0 x--2+ lim f(x) =-3+ %3D X00 f(-7) = 3 f'(-4) = 0 f(-6) = 0 f'(-1) = 0 f(-4) = -2 f'(1) DNE f(-1) = 0 f"(-6) = 0 f(1) = 3 f"(-4) = 0 f(2) = 0 f'(x) > 0 on x E (-1,1) f'(x) < 0 on x E (-, –2) U (–2, -1) U (1, 0) f"(x) > 0 on x E (-6, –4) U (–2, ∞) f"(x) < 0 on x E (-0, –6) U (-4, –2)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Use the information provided to sketch an accurate curve

lim_ f(x) =-0 lim f(x) = ∞ x→-2+ lim f(x) =-3+ x--2- X00 f(-7) = 3 f'(-4) = 0 f(-6) = 0 f'(-1) = 0 f(-4) = -2 f'(1) DNE f(1) = 3 f"(-4) = 0 f(2) = 0 f(-1) = 0 f"(-6) = 0 f' (x) > 0 on x E (-1,1) f'(x) < 0 on x € (-0,–2) U (-2, –1) U (1, ∞) f"(x) > 0 on x E (-6, –4) U (-2, 0) f"(x) < 0 on x E (-00, -6) U (–4, –2)
Transcribed Image Text:lim_ f(x) =-0 lim f(x) = ∞ x→-2+ lim f(x) =-3+ x--2- X00 f(-7) = 3 f'(-4) = 0 f(-6) = 0 f'(-1) = 0 f(-4) = -2 f'(1) DNE f(1) = 3 f"(-4) = 0 f(2) = 0 f(-1) = 0 f"(-6) = 0 f' (x) > 0 on x E (-1,1) f'(x) < 0 on x € (-0,–2) U (-2, –1) U (1, ∞) f"(x) > 0 on x E (-6, –4) U (-2, 0) f"(x) < 0 on x E (-00, -6) U (–4, –2)
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