document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=83450>Question 83450</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An open-top box is to be constructed from a 6 foot by 8 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.\r<BR>\n" );
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document.write( "a.Find the function V that represents the volume of the box in terms of x.\r<BR>\n" );
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document.write( "b.Graph this function and show the graph over the valid range of the variable x.\r<BR>\n" );
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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 #59954 by </B><A HREF=/tutors/aboutme.mpl?userid=Nate><B>Nate(3500)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Nate><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=59954\">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 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. <BR>\n" );
document.write( "Dimensions:<BR>\n" );
document.write( "Length = 8 - 2x<BR>\n" );
document.write( "Width = 6 - 2x<BR>\n" );
document.write( "Height = x<BR>\n" );
document.write( "a.Find the function V that represents the volume of the box in terms of x.<BR>\n" );
document.write( "V(x) = l*w*h = (8 - 2x)(6 - 2x)(x) = 48x - 28x^2 + 4x^3<BR>\n" );
document.write( "b.Graph this 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%28300%2C300%2C-1%2C5%2C-6%2C26%2C48x+-+28x%5E2+%2B+4x%5E3%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-1%2C5%2C-6%2C26%2C48x+-+28x%5E2+%2B+4x%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "c. Using the graph, what is the value of x that will produce the maximum volume?<BR>\n" );
document.write( "Seems when x = 1 ... max volume is 24ft^3 </SPAN>\n" );
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