Question 628271
What is the maximum volume of a open box created from a square of side length 24? Keep in mind that V=LWH. So for this problem the dimensions are as follows:
L = 24-2x, W = 24-2x and H = x. The maximum volume will be where the volume equation is the greatest.
-----------------
{{{V = (24-2x)^2*x = 4x^3 - 96x^2 + 576x}}}
{{{dV/dx = 12x^2 - 192x = 0}}}
x = 4
---------------
V(4) = 256 cubic units
--------------------------------