document.write( "Question 77542: An open-top box is to be constructed from a 4 foot by 6 foot rectangular cardboard by cutting out equal squares at each corner and folding up the flaps. Let x denote the length of each side of the square to be cut out.
\n" ); document.write( "a) Find the function V that represents the volume of the box in terms of x.\r
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\n" ); document.write( "\n" ); document.write( "b) Graph this function and show the graph over the valid range of the variable x..\r
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\n" ); document.write( "\n" ); document.write( "c) Using the graph, what is the value of x that will produce the maximum volume?\r
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Algebra.Com's Answer #55665 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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An open-top box is to be constructed from a 4 foot by 6 foot rectangular cardboard by cutting out equal squares at each corner and folding up the flaps. Let x denote the length of each side of the square to be cut out.
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\n" ); document.write( "The dimensions of the box will be (4-2x) by (6-2x) by x
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\n" ); document.write( "a) Find the function V that represents the volume of the box in terms of x.
\n" ); document.write( "V = (4-2x)*(6-2x)*x
\n" ); document.write( "V = 4x^3 - 20x^2 + 24x
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\n" ); document.write( "b) Graph this function and show the graph over the valid range of the variable x..
\n" ); document.write( " $\"+graph%28+300%2C+200%2C+-1%2C+2%2C+-10%2C+20%2C+4x%5E3+-+20x%5E2+%2B+24x%29+\"$
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\n" ); document.write( "c) Using the graph, what is the value of x that will produce the maximum volume?
\n" ); document.write( "It is about .8 ft or about 9.6 inches.
\n" ); document.write( "Max vol would be 2.4 * 4.4 * .8 = 8.45 cu ft \n" ); document.write( "

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