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September 22, 2014

September 22, 2014

Posted by **andy** on Thursday, July 19, 2012 at 9:13pm.

- math volume -
**drwls**, Thursday, July 19, 2012 at 9:33pmAre you allowed to use differential calculus?

Write an expression for box volume V in terms of the length of the corner cutouts, x.

V = (5-2x)(8-2x)*x

= 4x^3 -26x^2 +40x

Solve for x where V'(x) = dV/dx = 0

dV/dx = 12 x^2 -52x + 40 = 0

3x^2 -13x +10 = 0

x = (1/6)[13 +/- 7] = 1 and 3.333

The second root is not possible, because the removed material would exceed the length of the 5' side.

The largest volume is what you get with x = 1 foot.

Vmax = 18 ft^3

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