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Suppose f(x) is a function with the following properties: · ƒ"(−1) = ƒ"(0) = ƒ”(1) = 0, › ƒ"(x) > 0 for all x on(-∞, −1) U (1, ∞), and • ƒ"(x) < 0 for all ï on(–1, 0) U (0, 1). Which of the following is always TRUE? ƒ has exactly two inflection points which occur at x = 0 and x = 1. ƒ has exactly two inflection points which occur at x = −1 and x = 1. f has exactly three inflection points which occur at x = −1, x = 0, and x = 1. ƒ does not have any inflection points. Of has exactly two inflection points which occur at x = −1 and x = 0.

Suppose f(x) is a function with the following properties: · ƒ"(−1) = ƒ"(0) = ƒ”(1) = 0, › ƒ"(x) > 0 for all x on(-∞, −1) U (1, ∞), and • ƒ"(x) < 0 for all ï on(–1, 0) U (0, 1). Which of the following is always TRUE? ƒ has exactly two inflection points which occur at x = 0 and x = 1. ƒ has exactly two inflection points which occur at x = −1 and x = 1. f has exactly three inflection points which occur at x = −1, x = 0, and x = 1. ƒ does not have any inflection points. Of has exactly two inflection points which occur at x = −1 and x = 0.

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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Suppose f(x) is a function with the following properties: ƒ"(−1) = ƒ"(0) = ƒ”(1) = 0, • ƒ"(x) > 0 for all ï on(−∞, −1) U (1, ∞), and • ƒ"(x) < 0 for all ä on(–1, 0) U (0, 1). Which of the following is always TRUE? f has exactly two inflection points which occur at x = 0 and x = 1. ƒ has exactly two inflection points which occur at x = −1 and x = 1. f has exactly three inflection points which occur at x = − 1, x = 0, and x = 1. f does not have any inflection points. Of has exactly two inflection points which occur at x = -1 and x = 0.
Transcribed Image Text:Suppose f(x) is a function with the following properties: ƒ"(−1) = ƒ"(0) = ƒ”(1) = 0, • ƒ"(x) > 0 for all ï on(−∞, −1) U (1, ∞), and • ƒ"(x) < 0 for all ä on(–1, 0) U (0, 1). Which of the following is always TRUE? f has exactly two inflection points which occur at x = 0 and x = 1. ƒ has exactly two inflection points which occur at x = −1 and x = 1. f has exactly three inflection points which occur at x = − 1, x = 0, and x = 1. f does not have any inflection points. Of has exactly two inflection points which occur at x = -1 and x = 0.
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