Suppose ƒ : R → R is differentiable, f(0) = 0 and f'(x) > f(x) for all x ≥ 0. 1. Prove that f(x) > 0 on (0, a] for some a > 0. 2. Prove that f(x) > 0 for all x > 0.

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter3: The Derivative
Section3.CR: Chapter 3 Review
Problem 12CR: Determine whether each of the following statements is true or false and explain why. The derivative...
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Suppose ƒ : R → R is differentiable, f(0) = 0 and ƒ'(x) > ƒ(x) for all x ≥ 0.
1. Prove that f(x) > 0 on (0, a] for some a > 0.
2. Prove that f(x) > 0 for all x > 0.
Transcribed Image Text:Suppose ƒ : R → R is differentiable, f(0) = 0 and ƒ'(x) > ƒ(x) for all x ≥ 0. 1. Prove that f(x) > 0 on (0, a] for some a > 0. 2. Prove that f(x) > 0 for all x > 0.
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