2. Show that the following functions are convex by verifying the condition that² f(x) 20is satisfied for all a in the domain of f:(a) f(u₁, ₂) In(e" + e"),(b) f(ui, u2, U3, U₁)=-In(1-u₁-u2-uz-ua) over the domain {ue R4 | u₁+U₂+uz+us < 1}.

Answered: Image /qna-images/answer/17640e9b-ee92-40fb-aa0d-77dcf5ee2b2e.jpg

Answered: 2. Show that the following functions…

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter5: Graphs And The Derivative

Section5.3: Higher Derivatives, Concavity, And The Second Derivative Test

Problem 61E

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2. Show that the following functions are convex by verifying the condition that V² f(x) 20 is satisfied for all a in the domain of f: (a) f(un, u₂) In(e" + e"), (b) f(u, uz, us, UA) -In(1-₁-2-3-4) over the domain {u E R¹|u₁+uz+us+u₁ < 1}.