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Let f :-1, 1] -→ R be a three times differentiable function such that f(-1) = 0, f(0) = 0, f(1) = 1 and f' (0) = 0. Prove that f" (c) > 3 for some c E (-1, 1). %3D

Let f :-1, 1] -→ R be a three times differentiable function such that f(-1) = 0, f(0) = 0, f(1) = 1 and f' (0) = 0. Prove that f" (c) > 3 for some c E (-1, 1). %3D

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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Let f : [-1, 1] –→ R be a three times differentiable function such that f(-1) = 0, f(0) = = 0, f(1) = 1 and f'(0) = 0. Prove that f" (c) > 3 for somecE (-1,1).
Transcribed Image Text:Let f : [-1, 1] –→ R be a three times differentiable function such that f(-1) = 0, f(0) = = 0, f(1) = 1 and f'(0) = 0. Prove that f" (c) > 3 for somecE (-1,1).
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