GGQ. VII. 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)= +00, lim f(x)=0, lim f(x) = 0, and x4-2 8418 the table of signs for f' and f" is given below: (-∞,-2)-2 (-2,-1) -1 (-1,0) 0 (0,2) 2 (2+0) + dne - + dne + + dne + 0 f"(x) + dne + 0 - 1. Give the equations of all the linear asymptotes of the graph of f. 2. Determine the intervals where f is increasing or decreasing and where f is concave up or concave down. Identify the relative extremum points and points of inflection, if there are any. 3. Sketch the graph of f with emphasis on concavity. Label all the intercept points, rel- ative extremum points, and inflection points with their respective coordinates, and the asymptotes with their respective equations.
GGQ. VII. 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)= +00, lim f(x)=0, lim f(x) = 0, and x4-2 8418 the table of signs for f' and f" is given below: (-∞,-2)-2 (-2,-1) -1 (-1,0) 0 (0,2) 2 (2+0) + dne - + dne + + dne + 0 f"(x) + dne + 0 - 1. Give the equations of all the linear asymptotes of the graph of f. 2. Determine the intervals where f is increasing or decreasing and where f is concave up or concave down. Identify the relative extremum points and points of inflection, if there are any. 3. Sketch the graph of f with emphasis on concavity. Label all the intercept points, rel- ative extremum points, and inflection points with their respective coordinates, and the asymptotes with their respective equations.
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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VII. 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)= +00, lim f(x)=0, lim f(x) = 0, and
X4-2
8418
the table of signs for f' and f" is given below:
(-∞,-2)-2 (-2,-1) -1 (-1,0) 0 (0,2) 2 (2+0)
+
dne
+
dne + +
dne + 0
f"(x)
+
dne
+
0
1. Give the equations of all the linear asymptotes of the graph of f.
2. Determine the intervals where f is increasing or decreasing and where f is concave up or
concave down. Identify the relative extremum points and points of inflection, if there are
any.
3. Sketch the graph of f with emphasis on concavity. Label all the intercept points, rel-
ative extremum points, and inflection points with their respective coordinates, and the
asymptotes with their respective equations.
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