document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=73932>Question 73932</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 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.<BR>\n" );
document.write( "a)find the function V that represents the volume of the box in terms of x<BR>\n" );
document.write( "b) graph the function and show the graph over the valid range of the variable x<BR>\n" );
document.write( "c) Using the graph, what is the value of x that will produce the maximum volume? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #52924 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=52924\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 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.<BR>\n" );
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document.write( "Draw the picture so you can see the width, length, and height of the box.<BR>\n" );
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document.write( "a)find the function V that represents the volume of the box in terms of x<BR>\n" );
document.write( "New width is 6-2x ft , New length is 8-2x ft ; height = x ft.<BR>\n" );
document.write( "Volume = width*length*height <BR>\n" );
document.write( "V = (6-2x)(8-2x)x<BR>\n" );
document.write( "V = 4(3-x)(4-x)x<BR>\n" );
document.write( "V = 4x(x^2-7x+12)<BR>\n" );
document.write( "V = 4x^3-28x^2+48x<BR>\n" );
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document.write( "b) graph the function and show the graph over the valid range of the variable x<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C300%2C-2%2C3%2C-2%2C30%2C4x%5E3-29x%5E2%2B48x%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C300%2C-2%2C3%2C-2%2C30%2C4x%5E3-29x%5E2%2B48x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "c) Using the graph, what is the value of x that will produce the maximum volume?<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );