Question regarding optimization using calculus. Specifically, how to decide what to restrict your domain to

Question

Question regarding optimization using calculus.  Specifically, how to decide what to restrict your domain to

anonymous · Answer

An open top box is to be made by cutting small congruent squares from the corners of a 12in by 12in sheet of tin and bending up the sides

how I determine the domain?

anonymous · Answer

$$0 \le x \le 6$$

anonymous · Answer

I understand 0, but how do they determine 6?

anonymous · Answer

the reason i ask is to calculate endpoints.  the math computation isnt really the problem.  they want max area in this one... but I can find that.

hartnn · Answer

|dw:1366643392056:dw|
those squares are supposed to be congruent.
see, if x = 6 , then there will be no base left. 
if x>6 , the squares will overlap, which does't make sense. 
try imagining in your mind by increasing the size of squares....