Let f(x) be a function which is twice differentiable with f"(x) > 0 on the interval [a - 1, a + 1] and f(a) = 0. Prove that there exists some c ER with le-a < 1 such that f"(c) > f(a-1) + f(a+1) 2
Let f(x) be a function which is twice differentiable with f"(x) > 0 on the interval [a - 1, a + 1] and f(a) = 0. Prove that there exists some c ER with le-a < 1 such that f"(c) > f(a-1) + f(a+1) 2
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(x) be a function which is twice differentiable with f"(x) > 0 on the interval
[a 1, a + 1] and f(a) = 0. Prove that there exists some c ER with le-a| < 1 such that
f"(c) >
f(a-1) + f(a + 1)
2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F41e1d4c3-e4f3-464f-92a4-8d8edead8631%2F057106c0-0b41-4826-a495-d9b45749ccce%2Fs041f6o_processed.png&w=3840&q=75)
Transcribed Image Text:Let f(x) be a function which is twice differentiable with f"(x) > 0 on the interval
[a 1, a + 1] and f(a) = 0. Prove that there exists some c ER with le-a| < 1 such that
f"(c) >
f(a-1) + f(a + 1)
2
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