Maximum volume of open top box without calculus
By John Campbell •
A $5\times6$ piece of paper has squares of side-length $x$ cut from each of its corners, such that folding up the sides will create a box with no top. Find the value of $x$ that maximizes the volume of the open-top box without using calculus. I got the volume of the open top box is $V(x)=(5-2x)(6-2x)x=4x^3-22x^2+30x.$ From here, how to find $x?$
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