Let f be analytic and let f'(z) ‡ 0 on an open region N, and let zo E Nsuch that f(zo) ‡ 0. Prove that given € > 0 there exist 21, 22 € N such that|21 — 20 < €,22-20 < €and|ƒ(21)| > |ƒ(20)|, |ƒ(22)|<|ƒ(20)|.

Function f(z) is analytic in an open region Ω. The derivative f'(z) is non-zero for all z in Ω.…

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Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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Let f be analytic and let f'(z) ‡0 on an open region N, and let zo EN such that f(zo) # 0. Prove that given € > 0 there exist 21, 22 EN such that 21 -20 < €, |22-20 < € and |ƒ(21)| > |ƒ(zo), f(22)|