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Q3 1 Point Assume that f: R → R is differentiable, that f(0) = 0 and that f'(0) = 1. Which, if any, of the following statements necessarily follow? Choose all that apply. Of is strictly increasing. Of is increasing. There exists € > 0 such that f is increasing on (-€, €). There exists x > 0 such that f(x) > 0. f is not decreasing. None of these necessarily follow.

Q3 1 Point Assume that f: R → R is differentiable, that f(0) = 0 and that f'(0) = 1. Which, if any, of the following statements necessarily follow? Choose all that apply. Of is strictly increasing. Of is increasing. There exists € > 0 such that f is increasing on (-€, €). There exists x > 0 such that f(x) > 0. f is not decreasing. None of these necessarily follow.

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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Q3 1 Point Assume that f: R → R is differentiable, that f(0) = 0 and that f'(0) = 1. Which, if any, of the following statements necessarily follow? Choose all that apply. Of is strictly increasing. Of is increasing. There exists € > 0 such that f is increasing on (-€, €). There exists x > 0 such that f(x) > 0. f is not decreasing. None of these necessarily follow.
Transcribed Image Text:Q3 1 Point Assume that f: R → R is differentiable, that f(0) = 0 and that f'(0) = 1. Which, if any, of the following statements necessarily follow? Choose all that apply. Of is strictly increasing. Of is increasing. There exists € > 0 such that f is increasing on (-€, €). There exists x > 0 such that f(x) > 0. f is not decreasing. None of these necessarily follow.
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