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Consider the following proposed variation of Rolle's theorem. Let f: (a, b) → R be a differentiable function such that lim f(x) = ∞ and lim f(x) = ∞o. Then there exists a point c in the interval (a, b) such that f'(c) = 0. True or false: The proposed theorem is valid. O True False

Consider the following proposed variation of Rolle's theorem. Let f: (a, b) → R be a differentiable function such that lim f(x) = ∞ and lim f(x) = ∞o. Then there exists a point c in the interval (a, b) such that f'(c) = 0. True or false: The proposed theorem is valid. O True False

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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Consider the following proposed variation of Rolle's theorem. Let f: (a, b) → R be a differentiable function such that lim f(x) = ∞ and lim f(x) = ∞o. Then there exists a point c in the interval (a, b) such that f'(c) = 0. True or false: The proposed theorem is valid. True O False
Transcribed Image Text:Consider the following proposed variation of Rolle's theorem. Let f: (a, b) → R be a differentiable function such that lim f(x) = ∞ and lim f(x) = ∞o. Then there exists a point c in the interval (a, b) such that f'(c) = 0. True or false: The proposed theorem is valid. True O False
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