Suppose that a function f(x) satisfies the following properties, together with the table of signs given pelow. • f R\{2, –2} lim [f(x) – (x + 1)] = 0 is continuous on • lim f(x) = -∞ f(1.5) = f(3) = lim [f(r) – (x + 1)] = 0 lim f(x) = 2 T-2 T -00 -00, -3) -3 (-3, –2) -2 (-2,0) (0, 2) 2 (2, +0) f (x) f'(x) f"(x) und 3 und und und und und und und 1. Identify the equations of all the linear asymptotes of f. 2. Determine the intervals where the graph of f increasing/decreasing and concave up/down. 3. Identify the relative maximum/minimum points and points of inflection of f, if any. 4. Sketch a possible graph of f with emphasis on concavity. Label asymptotes with their equations and label all relevant points with their coordinates.
Suppose that a function f(x) satisfies the following properties, together with the table of signs given pelow. • f R\{2, –2} lim [f(x) – (x + 1)] = 0 is continuous on • lim f(x) = -∞ f(1.5) = f(3) = lim [f(r) – (x + 1)] = 0 lim f(x) = 2 T-2 T -00 -00, -3) -3 (-3, –2) -2 (-2,0) (0, 2) 2 (2, +0) f (x) f'(x) f"(x) und 3 und und und und und und und 1. Identify the equations of all the linear asymptotes of f. 2. Determine the intervals where the graph of f increasing/decreasing and concave up/down. 3. Identify the relative maximum/minimum points and points of inflection of f, if any. 4. Sketch a possible graph of f with emphasis on concavity. Label asymptotes with their equations and label all relevant points with their coordinates.
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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Number 1
![Suppose that a function f(x) satisfies the following properties, together with the table of signs given
below.
lim [f(x) – (x + 1)] = 0
lim f(x):
• f
is
continuous
on
= -0
X +00
R\{2, –2}
• f(1.5) = f(3) = 0
lim [f(x) – (x + 1)] = 0
lim f(x) = 2
T -00
x -2
(-∞, –3)
-3
(-3, –2)
-2
(-2,0)
(0, 2)
2
(2, +0)
f(x)
f'(x)
f" (x)
und
3.
und
+
und
und
+
und
+
und
und
und
1. Identify the equations of all the linear asymptotes of f.
Determir
the intervals where the graph of f increasing/decreasing and concave up/down.
3. Identify the relative maximum/minimum points and points of inflection of f, if any.
4. Sketch a possible graph of f with emphasis on concavity. Label asymptotes with their equations
and label all relevant points with their coordinates.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff2b07e6b-a666-4d80-ad1e-14b2a4ba5f15%2F45562889-bfa8-4798-abe8-5a924aff12fa%2Ffipwswr_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose that a function f(x) satisfies the following properties, together with the table of signs given
below.
lim [f(x) – (x + 1)] = 0
lim f(x):
• f
is
continuous
on
= -0
X +00
R\{2, –2}
• f(1.5) = f(3) = 0
lim [f(x) – (x + 1)] = 0
lim f(x) = 2
T -00
x -2
(-∞, –3)
-3
(-3, –2)
-2
(-2,0)
(0, 2)
2
(2, +0)
f(x)
f'(x)
f" (x)
und
3.
und
+
und
und
+
und
+
und
und
und
1. Identify the equations of all the linear asymptotes of f.
Determir
the intervals where the graph of f increasing/decreasing and concave up/down.
3. Identify the relative maximum/minimum points and points of inflection of f, if any.
4. Sketch a possible graph of f with emphasis on concavity. Label asymptotes with their equations
and label all relevant points with their coordinates.
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