# Differentiation, related rates?

## Homework Statement

Determine the dimensions of the rectangle of largest area that can be inscribed in the right triangle shown?

## The Attempt at a Solution

I've been trying to do this problem. I looked online and saw an explanation without directly using the area of the triangle, found http://answers.yahoo.com/question/index?qid=20101128161728AA21pl7".

Can someone remind me how to differentiate A = x H - (H/X)x^2 , in the last part of the problem? Is this from related rates?

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lCBl = X

lABl = H

H/h = X/x

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HallsofIvy
As far as differentiating Hx- (H/X)x2, one of the very first derivative rules you learned is that the derivative of $x^n$ is $nx^{n-1}$. However, you don't really need to use the derivative to maximize this. Complete the square to find the vertex of the parabola.