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.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.1: Inverse Functions
Problem 18E
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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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