(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A box with a square base and an open top has a volume of 4500cm^3. What are the dimensions of the box that will minimize the amount of material used? (Remember that the amount of material used refers to the surface area of the box).

My buddy and I spent a solid hour on this questions with no luck. Please help!

2. Relevant equations

No set equations, make your own.

3. The attempt at a solution

First we set our variables:

Let x=a side of the base

Let y=height of the box

Then we isolated the y variable:

x*x*y=4500

x^2*y=4500

y=4500/x^2

Then we made a surface area equation:

S(x)=x^2 + 4xy

S(x)=x^2 + 4x(4500/x^2)

S(x)=x^2 + 18000x/x^2

Then we multiplied everything by x^2 to get rid of the denominator to get:

S(x)=x^4 + 18000x

S(x)=x(x^3 + 18000)

Then we found the derivative of this equation:

S'(x)=4x^3 + 18000

S'(x)=4(x^3 + 4500)

This is where we got stuck because the critical number will be negative. Please help, we do not know what we did wrong.

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# Homework Help: Derivative Applications Question (High-school Calculus)

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