Question 33298
Starting with the formula for the volume of a rectangular prism (a box):
{{{V = L*W*h}}} The height of the box will be just x. The length, after cutting an x-square from each corner, will be 8-2x and the width will be 6-2x.
Now we can write the function (V) of the volume in terms of x.
{{{V = (8-2x)(6-2x)x}}} Simplify.
{{{V = 4x^3 - 28x^2 + 48x}}} This is the required function.

The graph is:
{{{graph(300,200,-5,5,-10,30,4x^3-28x^2+48x)}}}

By inspection, the maximum volume occurs at approximately x = 1