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Inequality with Differentiation

  • #1
159
0

Homework Statement


Let p > 1, and put q = p/(p-1), so 1/p + 1/q = 1. Show that for any x > 0, y > 0, we have

xy <= xp/p + yq/q, and find the case where equality holds.

Homework Equations



The Attempt at a Solution


This is in the differentiation chapter of my analysis book (Browder), so I'm going to go out on a limb here and assume that some aspect of differentiation comes into play here. Unfortunately, I don't really know how to start. Could someone get me started here? Thanks!
 

Answers and Replies

  • #2
73
1
Maybe try to find the minimum possible value of f(x,y)=x^p/p + y^q/q -xy
 

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