document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=86483>Question 86483</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 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.<BR>\n" );
document.write( "a) 	Find the function V that represents the volume of the box in terms of x.<BR>\n" );
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document.write( "b) 	Graph this function and show the graph over the valid range of the variable x..<BR>\n" );
document.write( "Show Graph here.\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?<BR>\n" );
document.write( "Answer.  <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #62595 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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/cgi-bin/show-face.mpl?user=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=62595\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 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.<BR>\n" );
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document.write( "We know from the above information:<BR>\n" );
document.write( "Box length = (6-2x)<BR>\n" );
document.write( "Box width = (4-2x)<BR>\n" );
document.write( "Box height = x<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( "Answer:<BR>\n" );
document.write( "Vol = length * width * height<BR>\n" );
document.write( "V = (6-2x)*(4-2x)*x<BR>\n" );
document.write( "V = x(24 - 20x + 4x^2); FOILed (6-2x)(4-2x); then mult by x<BR>\n" );
document.write( "V = 4x^3 - 20x^2 + 24x; represents the volume of the box<BR>\n" );
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document.write( "b) Graph this function and show the graph over the valid range of the variable x..<BR>\n" );
document.write( "Plot the value from .2 to 1.8 only; y = V<BR>\n" );
document.write( " x | y<BR>\n" );
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document.write( ".2 | 4.032<BR>\n" );
document.write( ".4 | 6.656<BR>\n" );
document.write( ".6 | 8.064<BR>\n" );
document.write( ".8 | 8.448<BR>\n" );
document.write( "1.0| 8.0<BR>\n" );
document.write( "1.2| 6.912<BR>\n" );
document.write( "etc<BR>\n" );
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document.write( "Show Graph here.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-1%2C+2%2C+-3%2C+10%2C+4x%5E3-20x%5E2%2B24x%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-1%2C+2%2C+-3%2C+10%2C+4x%5E3-20x%5E2%2B24x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\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?<BR>\n" );
document.write( "Answer.<BR>\n" );
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document.write( "It looks like max volume will occur when x = .8<BR>\n" );
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