Posted by John on Tuesday, November 27, 2012 at 6:01pm.
You are given a 12"x18" piece of construction paper. You are to cut a square out of each corner in order to create a 3dimensional opentop box. What size squares would you need to cut in order to maximize the volume of the box?

Precalculus  Reiny, Tuesday, November 27, 2012 at 6:13pm
let the side of the square to be cut out be x inches
resulting box is (122x) by (182x) by x
V = x(122x)(182x)= x(216  60x + 4x^2)
= 4x^3  60x^2 + 216x
dV/dx = 12x^2  120x + 216
= 0 for a max of V
x^2  10x + 18=0
solve for x

Precalculus  Damon, Tuesday, November 27, 2012 at 6:16pm
length = (18  2x)
width = (12  2x)
V = x (182x)(122x)
= x(4)(9x)(6x)
= 4 x (5415x+x^2)
= 4 (54 x 15x^2 + x^3)
dV/dx = 0 for max
0 = 54  30 x + 3 x^2
0 = 18  10 x + x^2
x = [ 10 +/ sqrt (10072) ]/2
[ 10 +/ 2 sqrt 7 ]/2
= 5 +/ sqrt 7
5+sqrt 7 is no good, more than half the width
so
5sqrt 7 = 2.35

Precalculus  Damon, Tuesday, November 27, 2012 at 6:18pm
Looks like calculus not precalculus to me by the way. I do not see how to do it without taking the derivative.

Precalculus  John, Tuesday, November 27, 2012 at 6:38pm
what does sqrt mean?
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