A box with no top is to be built by taking a 12 in -by 16-in sheet of card board, cutting x-inch square out of each corner and finding up the sides. Find the value of x that maximize the volume of the box
2 answers
The value of x that maximizes the volume of the box is 4 inches.
AAAaannndd the bot gets it wrong yet again!
4*8*4 = 128
v = (12-2x)(16-2x)x = 4x^3-56x^2+192x
dv/dx = 12x^2-112x+192
so max v is where dv/dx=0
that is when x = (14-2√13)/3 and v = 64/27 (35+13√13) = 194.07
4*8*4 = 128
v = (12-2x)(16-2x)x = 4x^3-56x^2+192x
dv/dx = 12x^2-112x+192
so max v is where dv/dx=0
that is when x = (14-2√13)/3 and v = 64/27 (35+13√13) = 194.07
2 answers