(adsbygoogle = window.adsbygoogle || []).push({}); Problem: An open top box is constructed from a sheet of material by cutting equal squares from each corner and folding up the edges. If thesheet of materialmeasures 14 inches by 9 inches, find the dimensionwhich represents the length of one side of the square that should be cut off so that the volume is maximized.x

Work Done (Please Check!):

Length: [tex]L(x)=-2x+14[/tex]

Width: [tex]W(x)=-2x+9[/tex]

Height: [tex]H(x)=x[/tex]

Volume: [tex]V(x)=4x^{3}-46x^{2}+126x[/tex]

This is where I am stuck:

[tex]V'(x)=12x^{2}-92x+126[/tex]

I need to factor out the derivative so that I can get the critical numbers. Unless I did something wrong, from what I got above it's not going to be whole numbers. I always have problems with fractions.

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# Homework Help: Need help on another optimization problem!

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