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Suppose that f has continuous derivative and is twice differentiable in R. Suppose that f(a) = f(b) = 0. Show that for every x E (a,b), there is § E (a,b) such that f"(€) (æ – a)(x – b). f(x) = 2

Suppose that f has continuous derivative and is twice differentiable in R. Suppose that f(a) = f(b) = 0. Show that for every x E (a,b), there is § E (a,b) such that f"(€) (æ – a)(x – b). f(x) = 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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Suppose that f has continuous derivative and is twice differentiable in R. Suppose that f(a) = f(b) = = 0. Show that for every x E (a, b), there is E (a, b) such that f"(£), (x – a) (x – 6). f(æ) = 2 Hint: let k = f(x)/(x – a)(x – b); consider the function F(t) = f(t) – k(x – a)(x – b) and use the first exercise.
Transcribed Image Text:Suppose that f has continuous derivative and is twice differentiable in R. Suppose that f(a) = f(b) = = 0. Show that for every x E (a, b), there is E (a, b) such that f"(£), (x – a) (x – 6). f(æ) = 2 Hint: let k = f(x)/(x – a)(x – b); consider the function F(t) = f(t) – k(x – a)(x – b) and use the first exercise.
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