# Inequality with Differentiation

## 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.

## 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!