SOLUTION: An open box is to be made from a square piece of material 36cm on a side by cutting equal squares from the corners and turning up the sides. See the following table: Height

Question 360564: An open box is to be made from a square piece of material 36cm on a side by cutting equal squares from the corners and turning up the sides. See the following table:
Height Width Volume
1 36- 2(1) 1[36-2(1)]^2 =1156
2 36- 2(2) 2[36-2(2)]^2 =2048
1. Verify that the volume of the box is given by V = x(36-2x)^2. Determine the domain of the function.
2. Use a graphing calculator to graph V, and use the range of dimensions from the table to find the x- value for which V(x) is maximum.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
1. Verify that the volume of the box is given by V = x(36-2x)^2. Determine the domain of the function.
height = x
base is 36-2x by 36-2x
--------------------------
Domain:
Solve: 36-2x >= 0
2x <= 36
0<= x <= 18
---------------------
2. Use a graphing calculator to graph V, and use the range of dimensions from the table to find the x- value for which V(x) is maximum.
---
Maximum when x = 6
=========================
Cheers,
Stan H.
RELATED QUESTIONS
An open box is to be made from a square piece of material, mc001-1.jpg inches on a side,... (answered by addingup)

An open box made from a square piece of cardboard 14 inches on a side by cutting... (answered by greenestamps,josgarithmetic,ikleyn)

An open box is to be made from a flat square piece of material 15 inches in length and... (answered by stanbon)

An open box is to be made from a 24 in. by 36 in. piece of cardboard by cutting out... (answered by josgarithmetic,ikleyn)

The exact problem as it shows up on my homework is: An open box of maximum volume is to... (answered by stanbon)

an open box is made from a rectangular piece of material 20"by 25" by cutting equal... (answered by checkley77)

A box with a square bottom and no top is to be made from a 6 by 6 - inch piece of... (answered by josgarithmetic,ikleyn)

An open box is made from a square piece of cardboard 46 inches on a side by cutting... (answered by josgarithmetic)

An open box is made from a square piece of sheet metal 19 inches on a side by cutting... (answered by stanbon)