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+ -1-1x the table of signs for f' and f" are given below: f'(x) f"(x) (-∞, -1) -1 (-1,1) 1 (1, 2) und. + 0 + und. 0 + 8+←æ 2 und. und. (2, +∞0) + b. 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.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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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.

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.
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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