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…

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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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