Re: [分析] 證明x^p/p + y^q/q >= 1/p + 1/q

[Sfly (topos)]

※ 引述《iddee ()》之銘言：
: 證明 (x^p)/p + (y^q)/q ≧ 1/p + 1/q
: for p,q > 1 and x,y > 0 with xy = 1

應該有別的方法, 但我的第一個想法是用mean-value定理來證

Suppose x>=1, y<=1, then log(x)=-log(y) >=0.

x^p-1   y^q-1
----- + ------  = x^(p')log(x) + y^(q')log(y)
p         q

                = (x^(p')- y^(q'))log(x) >=0.


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推 iddee       :好方法, good