Question 173211
A rectangular piece of metal 32cm by 22cm, has a square of side X cm removed
 from each corner in order to form a rectangular box. 
If the volume of the  box is to be a maximum what is the value of X?
:
From the given information we know the dimensions (L,W,H) of the box is:
(32-2x) by (22-2x) by x
:
Area = length * width * height
A = (32-2x) * (22 - 2x) * x
FOIL
A = x(704 - 64x - 44x + 4x^2) 
A = x(704 - 108x + 4x^2)
A = 704x - 108x^2 + 4x^3
or the standard arrangement is:
y = 4x^3 - 108x^2 + 704x
:
Plot this equation, we only are interested in the positive values x,y values 
{{{ graph( 300, 200, -6, 15, -500, 1600, 4x^3-108x^2+704x) }}}
:
Using my trusty Ti83, max volume occurs when x = 4.274 cm about 1348 cu/cm