Question 73932
An open top box is to be constructed from a 6 foot by 8 foot rectanglar cardboard by cutting out equal squares at each corner and the folding up the flaps. Let x denote the length of each side of the square to be cut out.
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Draw the picture so you can see the width, length, and height of the box.
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a)find the function V that represents the volume of the box in terms of x
New width is 6-2x ft , New length is 8-2x ft ; height = x ft.
Volume = width*length*height 
V = (6-2x)(8-2x)x
V = 4(3-x)(4-x)x
V = 4x(x^2-7x+12)
V = 4x^3-28x^2+48x
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b) graph the function and show the graph over the valid range of the variable x
{{{graph(400,300,-2,3,-2,30,4x^3-29x^2+48x)}}}
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c) Using the graph, what is the value of x that will produce the maximum volume?
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Cheers,
Stan H.