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Suppose that f is continuous on [a, b], f (a) exists, and µ is between f(a) and (f(b) f(a))/(b-a). Show that f(c) = f(a) = µ(ca) for some c in (a, b). -

Suppose that f is continuous on [a, b], f (a) exists, and µ is between f(a) and (f(b) f(a))/(b-a). Show that f(c) = f(a) = µ(ca) for some c in (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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17. Suppose that f is continuous on [a, b], ƒ (a) exists, and µ is between f(a) and (ƒ(b) – ƒ(a))/(b − a). Show that f(c) — f(a) = µ(c − a) for some c in (a, b).
Transcribed Image Text:17. Suppose that f is continuous on [a, b], ƒ (a) exists, and µ is between f(a) and (ƒ(b) – ƒ(a))/(b − a). Show that f(c) — f(a) = µ(c − a) for some c in (a, b).
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