Help Min & max applied problems

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Homework Statement


An open box with a square base is to be constructed from 3 square feet of material. What dimensions will produce a box with maximun volume?


Homework Equations



v = l * w * h

The Attempt at a Solution



any other formulas involved.. ?

help... and thanx!
 
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Since you want to maximize volume you're going to want to take the derivative of V. In order to do that you first need to get it in terms of a single variable. To do this you need a second equation relating either length width or height to some number. In your case you would want to write the equation giving the surface area of the box and go from there. Hope this helps
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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