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c) Consider the function f defined by { f(x) = ex-1 X 1 if x ‡ 0 if x = 0 (i) Prove that f is differentiable at 0 and find its derivative the (ii) Show that f' is non-negative at all points other than 0.

c) Consider the function f defined by { f(x) = ex-1 X 1 if x ‡ 0 if x = 0 (i) Prove that f is differentiable at 0 and find its derivative the (ii) Show that f' is non-negative at all points other than 0.

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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[18 Q3] A question about differentiability :)

c) Consider the function f defined by f(x) = ex - 1 X 1 if x #0 if x = 0 (i) Prove that f is differentiable at 0 and find its derivative there. (ii) Show that f' is non-negative at all points other than 0.
Transcribed Image Text:c) Consider the function f defined by f(x) = ex - 1 X 1 if x #0 if x = 0 (i) Prove that f is differentiable at 0 and find its derivative there. (ii) Show that f' is non-negative at all points other than 0.
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