2. Consider the function f that satisfies the following: f is continuous everywhere except at x = - -1,2, f has an x-intercept at x = 1, f has a y-intercept at y = −1, lim_ f(x) = ==∞ = lim f(x), lim f(x) = +∞ = lim f(x), lim f(x) = 0, and x→-1+ x-2- x→2+ x→±x -I--x • the table of signs for f' and f" are given below: (-∞, -1) f'(x) f"(x) -1 (-1, 1) und. + und. 1 0 0 (1,2) + + 2 und. und. (2, +∞) + b. Determine the intervals where f is increasing or decreasing and where ƒ is concave up or concave down. Identify the relative extremum points and points of inflection, if there are any.
2. Consider the function f that satisfies the following: f is continuous everywhere except at x = - -1,2, f has an x-intercept at x = 1, f has a y-intercept at y = −1, lim_ f(x) = ==∞ = lim f(x), lim f(x) = +∞ = lim f(x), lim f(x) = 0, and x→-1+ x-2- x→2+ x→±x -I--x • the table of signs for f' and f" are given below: (-∞, -1) f'(x) f"(x) -1 (-1, 1) und. + und. 1 0 0 (1,2) + + 2 und. und. (2, +∞) + b. Determine the intervals where f is increasing or decreasing and where ƒ is concave up or concave down. Identify the relative extremum points and points of inflection, if there are any.
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
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.
Transcribed Image Text:2. Consider the function f that satisfies the following:
f is continuous everywhere except at x = -1,2,
f has an x-intercept at x = 1,
:-1,
f has a y-intercept at y
lim f(x)= ==∞ = lim f(x), lim f(x) = +∞
x-2-
x→-1-
+l-←x
the table of signs for f' and f" are given below:
|f'(x)
f"(x)
(-∞, -1) -1 (−1,1)
und.
+
und.
=
lim f(x), lim f(x) = 0, and
x→2+
x →±∞
1 (1,2)
0 +
0 +
2 (2, +∞)
und.
und.
+
b.
Determine the intervals where ƒ 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.
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