A box with an open top is to be constructed from a square piece of cardboard, 6 meters wide, by cutting out a square from each of the four corners, and bending up the sides. Find the largest volume that such a box can have.

Let x represent the dimensions

$\displaystyle V = (6 - 2x)^2x$

$\displaystyle V = 36x - 24x^2 + 4x^{3}$

$\displaystyle V' = 36 - 48x + 12x^2$

$\displaystyle 0 = 36 - 48x + 12x^2$

$\displaystyle 0 = 12(x - 1)(x - 3)$

$\displaystyle x = 1 and x = 3$

Restrictions: $\displaystyle 0 \leq x \leq 3$

$\displaystyle V = Lwh$

$\displaystyle V = (3)(1)(6)$

$\displaystyle V = 18m^{3}$

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**Text Answer is $\displaystyle 16m^{3}$**
Please help me correct my work?