Consider the function f that satisfies the following: . f is continuous everywhere except at x = -2, • f(-1) = 0, f (0) = −3, f (2) = −1, and f(-2) is undefined, . lim f(x) = +∞, lim f(x) = 0, lim f(x) = 0, and X→-2 X→→→→+∞0 X→→→-00 . the table of signs for f' and f" is given below (-∞, -2) -2 (-2,-1) -1 0 f'(x) + dne dne f"(x) + dne + dne O (-1,0) (0,2) + + + 0 (2, +00)
Consider the function f that satisfies the following: . f is continuous everywhere except at x = -2, • f(-1) = 0, f (0) = −3, f (2) = −1, and f(-2) is undefined, . lim f(x) = +∞, lim f(x) = 0, lim f(x) = 0, and X→-2 X→→→→+∞0 X→→→-00 . the table of signs for f' and f" is given below (-∞, -2) -2 (-2,-1) -1 0 f'(x) + dne dne f"(x) + dne + dne O (-1,0) (0,2) + + + 0 (2, +00)
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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Question
Sketch the graph of f with emphasis on concavity. Label all the intercept points, relative extremum points, and inflection points with their respective coordinates, and the asymptotes with their respective equations.
Transcribed Image Text:Consider the function f that satisfies the following:
• fis continuous everywhere except at x = -2,
• f(-1) = 0, f (0) = −3, f (2) = -1, and f(-2) is undefined,
.
lim f(x) = +∞, lim f(x) = 0, lim f(x) = 0, and
X→-2
X→→→→→+∞0⁰
X-→-00
●
the table of signs for f' and f" is given below
f'(x)
f"(x)
(-∞, -2) -2 (-2,-1) -1 (-1,0)
dne
dne
+
0
+
+
0 (0,2) 2
dne
+
dne
+
0
(2, +00)
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