P.math In the following question, let f: R → R be a differentiable function. Now assume that ƒ(0) = 0 and ƒ'(0) = 0. Prove that if ƒ is twice differentiable and|f"(x)| ≤ 1 for all x ER thenVx≥ 0, f(x) ≤ 22.2

f:R--> R is a differentiable function.We assume that f(0) = 0 and f'(0) = 0 We need to prove that…

Answered: Now assume that f(0) |f"(x)| ≤ 1 for…

Now assume that f(0) |f"(x)| ≤ 1 for all x ER then = 0 and f'(0) = 0. Prove that if f is twice differentiable and Vx>0, f(x) ≤ 1/²2/ 2

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.

Chapter1: Functions

Section1.3: Properties Of Functions

Problem 1E

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P.math

Now assume that ƒ(0) = 0 and ƒ'(0) = 0. Prove that if ƒ is twice differentiable and
|f"(x)| ≤ 1 for all x ER then
Vx≥ 0, f(x) ≤ 22.
2

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