Answer:
Maximum volume = 649.519 cubic inches 
Step-by-step explanation:
A rectangular piece of cardboard of side 15 inches by 30 inches is cut in such that a square is cut from each corner. Let x be the side of this square cut. When it was folded to make the box the height of box becomes x, length becomes (30-2x) and the width becomes (15-2x).
Volume is given by  
V = 
First, we differentiate V(x) with respect to x, to get,

Equating the first derivative to zero, we get,

Solving, with the help of quadratic formula, we get,
 ,
,
Again differentiation V(x), with respect to x, we get,

At x = 
 ,
,

Thus, by double derivative test, the maxima occurs at 
x =  for V(x).
 for V(x).
Thus, largest volume the box can have occurs when  .
.
Maximum volume = 
