Question 498879
After removing the corner squares of side x, the remainder of the sides of the original rectangular cardboard will measure (40-2x) and (30-2x) and the height of the finished box will be x.
The volume of this box can be expressed as:
{{{V = (40-2x)(30-2x)x}}} If you multiply these factors, you'll get:
{{{V = 4x^3-140x^2+1200x}}}
Clearly, this is a "cubic" function.
From a practical standpoint, x cannot equal or exceed half the length of the smaller side of the original rectangle, otherwise, you could not make a box.
So x can take on values: {{{0<x<15}}}