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• f(0) = 1 ● lim f(x) = lim_ƒ(x) = 0 x →∞ x118 • The values of f'(x) and ƒ"(x) are as follows: f'(x) < 0 f'(x) > 0 x < -1 or x > 2 −1 < x < 2 ƒ" (x) < 0 | x < −2 or 0 < x < 4 ƒ" (x) > 0 −2 < x < 0 or x > 4 (a) Identify any horizontal asymptotes. (b) On what interval(s) is f(x) increasing?

• f(0) = 1 ● lim f(x) = lim_ƒ(x) = 0 x →∞ x118 • The values of f'(x) and ƒ"(x) are as follows: f'(x) < 0 f'(x) > 0 x < -1 or x > 2 −1 < x < 2 ƒ" (x) < 0 | x < −2 or 0 < x < 4 ƒ" (x) > 0 −2 < x < 0 or x > 4 (a) Identify any horizontal asymptotes. (b) On what interval(s) is f(x) increasing?

Advanced Engineering Mathematics
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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Let f (x) be a function which is twice-differentiable on R = (−∞, ∞) and which satisfies the following properties:

ƒ(0) = 1 ● lim f(x) = lim f(x) = 0 x →∞ 81个 • The values of f'(x) and f'(x) are as follows: f'(x) < 0 f'(x) > 0 x < -1 or x > 2 −1 < x < 2 ƒ"(x) < 0 f" (x) > 0 −2 < x < 0 or x > 4 x < -2 or 0 < x < 4 (a) Identify any horizontal asymptotes. (b) On what interval(s) is f(x) increasing? (c) At what x-value(s) does f(x) have a local minimum? (d) At what x-value(s) does f(x) have a local maximum? (e) On what interval(s) is f(x) concave up? (f) At what x-value(s) does f(x) have inflection point(s)? (g) Sketch the graph of f(x).
Transcribed Image Text:ƒ(0) = 1 ● lim f(x) = lim f(x) = 0 x →∞ 81个 • The values of f'(x) and f'(x) are as follows: f'(x) < 0 f'(x) > 0 x < -1 or x > 2 −1 < x < 2 ƒ"(x) < 0 f" (x) > 0 −2 < x < 0 or x > 4 x < -2 or 0 < x < 4 (a) Identify any horizontal asymptotes. (b) On what interval(s) is f(x) increasing? (c) At what x-value(s) does f(x) have a local minimum? (d) At what x-value(s) does f(x) have a local maximum? (e) On what interval(s) is f(x) concave up? (f) At what x-value(s) does f(x) have inflection point(s)? (g) Sketch the graph of f(x).
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