SOLUTION: an open- top box is to be made from an 8 in by 12 in rectangular piece of copper by cutting equal squares (x in by x in) from each corner and folding up the sides. write volume of

Question 194503: an open- top box is to be made from an 8 in by 12 in rectangular piece of copper by cutting equal squares (x in by x in) from each corner and folding up the sides. write volume of the box V as a function of x. use a graphing calculator to find the maximum possible volume to the nearest hundredth of a cubic inch. what are the final dimensions of this box?
I am having hard time for this problem. please help me please...... it is urgent for my midterm exam please.....

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
an open- top box is to be made from an 8 in by 12 in rectangular piece of copper by cutting equal squares (x in by x in) from each corner and folding up the sides. write volume of the box V as a function of x. use a graphing calculator to find the maximum possible volume to the nearest hundredth of a cubic inch. what are the final dimensions of this box?
:
Draw this out and you will see the dimensions of the box will be:
(8-2x) by (12-2x) by x
:
FOIL the length and width
96 - 16x - 24x + 4x^2
Write this
4x^2 - 40x + 96
Multiply this by the height (x) and you have the volume function
:
V(x) = 4x^3 - 40x^2 + 96x
:
Find the maximum volume on a graphing calc: enter: y = 4x^3 - 40x^2 + 96x
Scale x:-4,+8; y:-50, +150
Should look like this

You can see the max that we want is about x=1.6
Use the max feature on the calc to find the exact value of x and y(volume)
I got x = 1.57 in; y = 67.6 cu/in as the max volume
:
Sorry about that. If have any questions, email me. Carl

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