Home /
Expert Answers /
Calculus /
open-box-problem-an-open-box-top-open-is-made-from-a-rectangular-material-of-dimensions-a-8-inch-pa934

Open-box Problem. An open-box (top open) is made from a rectangular material of dimensions

`a=8`

inches by

`b=7`

inches by cutting a square of side

`x`

at each corner and turning up the sides (see the figure). Determine the value of

`x`

that results in a box the maximum volume. Following the steps to solve the problem. Check Show Answer only after you have tried hard. (1) Express the volume

`V`

as a function of

`x:V=`

(2) Determine the domain of the function

`V`

of

`x`

(in interval form): (3) Expand the function

`V`

for easier differentiation:

`V=`

(4) Find the derivative of the function

`V:V^(')=`

(5) Find the critical point(s) in the domain of

`V`

: (6) The value of

`V`

at the left endpoint is (7) The value of

`V`

at the right endpoint is (8) The maximum volume is

`V=`

(9) Answer the original question. The value of

`x`

that maximizes the volume is: