Consider x cm as the length cut off from each corner
So the length of box is (12 – 2x) cm and x cm as its breadth and height
Here volume can be written as
V = (12 – 2x)2 × x
On further simplification
V = 4x3 – 48x2 + 144x
By differentiating w.r.t. x
We know that V is maximum when x = 2
Here V = {(12 – 4)2 × 2} = {64 × 2} = 128 cm3