Question

a box with no top is to be built by taking a 12''-by-16'' sheet of cardboard and cutting x-inch squares our of each corner and folding up the sides. find the value of x that maximizes the volume of the box

Answer 1

If you cut out corner squares with length x , the height of the box is x and the base dimensions are (12-2x) * (16 - 2x)

Box volume V = x(12-2x)(16-2x)
(0 < x < 6)

V = 192x -56x^2 + 4x^3

Set the derivative dV/dx = 0 and solve for x

Answer 2

A box with no top is to be built by taking a 12 in -by 16-in sheet of cardboard, 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​

Answer 3

20