Inequality with Differentiation

[steelphantom]

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 <= x^p/p + y^q/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!

 

[grief]

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