1. Let f be a function satisfying the following properties: • continuous on R\{1} • f(0) = 0 and f(3) = 7 • lim f(x) = +o lim [f(x) – (x + 2)] = 0 lim [f(x) – (x + 2)] = 0 Moreover, the table of signs for f' and f" is given below. (-∞0, 0) | 0 | (0, 1) 1 (1,3) | 3 | (3,+∞ f'(r) f"(x) + + und. + + und. + + 1. Give equations of the two linear asymptotes of the graph of f. 2. Determine where is f increasing or decreasing and concave up or 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.
1. Let f be a function satisfying the following properties: • continuous on R\{1} • f(0) = 0 and f(3) = 7 • lim f(x) = +o lim [f(x) – (x + 2)] = 0 lim [f(x) – (x + 2)] = 0 Moreover, the table of signs for f' and f" is given below. (-∞0, 0) | 0 | (0, 1) 1 (1,3) | 3 | (3,+∞ f'(r) f"(x) + + und. + + und. + + 1. Give equations of the two linear asymptotes of the graph of f. 2. Determine where is f increasing or decreasing and concave up or 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.
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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![1. Let f be a function satisfying the following properties:
continuous on R \ {1}
lim [f(x) – (x+ 2)] = 0
f(0) = 0 and f(3) = 7
lim f(x) = +o
lim [f(x) – (x + 2)] = 0
Moreover, the table of signs for f' and f" is given below.
(-00,0) | 0 | (0, 1)
1
(1,3) | 3 | (3, +
f'(x)
f"(x)
+
und.
+
und.
+
1. Give equations of the two linear asymptotes of the graph of f.
2. Determine where is f increasing or decreasing and concave up or concave down. Determine
the relative maximum, relative minimum and inflection points of the graph of ƒ (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%2F4ed3802a-342d-423b-9be4-557c5c4bd1df%2Fc0c73228-5521-4d8a-9491-32e2174a792c%2Fn7prys_processed.png&w=3840&q=75)
Transcribed Image Text:1. Let f be a function satisfying the following properties:
continuous on R \ {1}
lim [f(x) – (x+ 2)] = 0
f(0) = 0 and f(3) = 7
lim f(x) = +o
lim [f(x) – (x + 2)] = 0
Moreover, the table of signs for f' and f" is given below.
(-00,0) | 0 | (0, 1)
1
(1,3) | 3 | (3, +
f'(x)
f"(x)
+
und.
+
und.
+
1. Give equations of the two linear asymptotes of the graph of f.
2. Determine where is f increasing or decreasing and concave up or concave down. Determine
the relative maximum, relative minimum and inflection points of the graph of ƒ (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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