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Assume f and g are both continuous on the closed interval [a, b), f(a) < g(a) and f(b) > g(b). Prove f (x) = g(x) for some point x € (a, b).

Assume f and g are both continuous on the closed interval [a, b), f(a) < g(a) and f(b) > g(b). Prove f (x) = g(x) for some point x € (a, b).

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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Assume \( f \) and \( g \) are both continuous on the closed interval \([a, b]\), \( f(a) < g(a) \) and \( f(b) > g(b) \). Prove \( f(x) = g(x) \) for some point \( x \in (a, b) \).
Transcribed Image Text:Assume \( f \) and \( g \) are both continuous on the closed interval \([a, b]\), \( f(a) < g(a) \) and \( f(b) > g(b) \). Prove \( f(x) = g(x) \) for some point \( x \in (a, b) \).
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