Differential Calculus Exercise Problem #1 Let f be a function satisfying the following properties: Continuous on R \ {0} f(-1) = -4 f0) = 1 and f (플)=: lim f(x) = 0 x-+00 lim [f(x) – (x – 2)] = 0 x--00 lim f(x) = 1 x-0+ lim f(x) = -∞ x-0 Moreover, the table of signs for f' and f" is given below. (-0, –1) -1 (-1,0) 2 0.58 V3 +00 f'(x) f"(x) иnd иnd + 1. Give equations of the three linear asymptotes of the graph of f. 2. Determine where is f increasing or decreasing and concave up and concave down. Determine the relative maximum, relative minimum, and inflection points of the graph of f (if any). 3. Sketch the graph of f with emphasis on concavity. Label all the relative extremum points, and inflection points with their respective coordinates, and the asymptotes with their respective eguations
Differential Calculus Exercise Problem #1 Let f be a function satisfying the following properties: Continuous on R \ {0} f(-1) = -4 f0) = 1 and f (플)=: lim f(x) = 0 x-+00 lim [f(x) – (x – 2)] = 0 x--00 lim f(x) = 1 x-0+ lim f(x) = -∞ x-0 Moreover, the table of signs for f' and f" is given below. (-0, –1) -1 (-1,0) 2 0.58 V3 +00 f'(x) f"(x) иnd иnd + 1. Give equations of the three linear asymptotes of the graph of f. 2. Determine where is f increasing or decreasing and concave up and concave down. Determine the relative maximum, relative minimum, and inflection points of the graph of f (if any). 3. Sketch the graph of f with emphasis on concavity. Label all the relative extremum points, and inflection points with their respective coordinates, and the asymptotes with their respective eguations
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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![Differential Calculus Exercise Problem #1
Let f be a function satisfying the following properties:
Continuous on R\ {0}
f(-1) = -4
3
f(0) = 1 and f () =
4
lim f(x) = 0
x+00
lim [f(x) – (x – 2)] = 0
X -00
lim f(x) = 1
lim f(x) =
-00
x-0-
Moreover, the table of signs for f' and f" is given below.
-со, —1)
-1
(-1,0)
* 0.58
V3
0,
V3
f'(x)
f"(x)
иnd
иnd
+
1. Give equations of the three linear asymptotes of the graph of f.
2. Determine where is f increasing or decreasing and concave up and concave down.
Determine the relative maximum, relative minimum, and inflection points of the graph of f (if
any).
3. Sketch the graph of f with emphasis on concavity. Label all the relative extremum points,
and inflection points with their respective coordinates, and the asymptotes with their
respective equations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F456fa68a-39f1-4fe9-b6e3-237a246a7d1a%2F924c4df9-3980-4013-90f7-4b7a205bee17%2F0pm052i_processed.png&w=3840&q=75)
Transcribed Image Text:Differential Calculus Exercise Problem #1
Let f be a function satisfying the following properties:
Continuous on R\ {0}
f(-1) = -4
3
f(0) = 1 and f () =
4
lim f(x) = 0
x+00
lim [f(x) – (x – 2)] = 0
X -00
lim f(x) = 1
lim f(x) =
-00
x-0-
Moreover, the table of signs for f' and f" is given below.
-со, —1)
-1
(-1,0)
* 0.58
V3
0,
V3
f'(x)
f"(x)
иnd
иnd
+
1. Give equations of the three linear asymptotes of the graph of f.
2. Determine where is f increasing or decreasing and concave up and concave down.
Determine the relative maximum, relative minimum, and inflection points of the graph of f (if
any).
3. Sketch the graph of f with emphasis on concavity. Label all the relative extremum points,
and inflection points with their respective coordinates, and the asymptotes with their
respective equations.
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