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3.17 Supposep<1, p # 0. Show that the function 1/p f(x) = ( i=1 with dom f = R+ is concave. This includes as special cases f(x) = (E"_, x;2)2 and the harmonic mean f(x) = (D 1/xi)-1. Hint. Adapt the proofs for the log-sum-exp

3.17 Supposep<1, p # 0. Show that the function 1/p f(x) = ( i=1 with dom f = R+ is concave. This includes as special cases f(x) = (E"_, x;2)2 and the harmonic mean f(x) = (D 1/xi)-1. Hint. Adapt the proofs for the log-sum-exp

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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3.17 Suppose p < 1, p # 0. Show that the function 1/p (E-) n f (x) = ? with dom f = R+ is concave. This includes as special cases f(x) = (E"_, x;12)² and the harmonic mean f(x) = (E" 1/x;)¬1. Hint. Adapt the proofs for the log-sum-exp function and the geometric mean in §3.1.5. %3D
Transcribed Image Text:3.17 Suppose p < 1, p # 0. Show that the function 1/p (E-) n f (x) = ? with dom f = R+ is concave. This includes as special cases f(x) = (E"_, x;12)² and the harmonic mean f(x) = (E" 1/x;)¬1. Hint. Adapt the proofs for the log-sum-exp function and the geometric mean in §3.1.5. %3D
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