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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

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

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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In the following question, let f: R → R be a differentiable function.
Transcribed Image Text: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 then Vx≥ 0, f(x) ≤ 22. 2
Transcribed Image Text: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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