document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1011095>Question 1011095</A>: <I><SPAN STYLE=\"word-break: break-all;\"> By cutting squares out of the corners of an 8 1/2 in x 11in sheet of paper, and folding up the edges, you can form a box. Whats the largest possible volume of the box if the length cut is no less than 1in and no more than 4 in? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #626672 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39630)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=626672\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Sidelength of the squares cut, x.<BR>\n" );
document.write( "v for volume, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v=x%288.5-2x%29%2811-2x%29 ALIGN=MIDDLE  ALT=\"v=x%288.5-2x%29%2811-2x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >;<BR>\n" );
document.write( "how?  Height x multiplied by the area of base formed  (8.5-2x)(11-2x).\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v=4x%5E3-%2822%2B19%29x%5E2%2B8.5%2A11x ALIGN=MIDDLE  ALT=\"v=4x%5E3-%2822%2B19%29x%5E2%2B8.5%2A11x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28v=4x%5E3-41x%5E2%2B93.5x%29 ALIGN=MIDDLE  ALT=\"highlight%28v=4x%5E3-41x%5E2%2B93.5x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >------general volume formula\r<BR>\n" );
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document.write( "FIND MAXIMUM\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dv%2Fdx=12x%5E2-82x%2B93.5 ALIGN=MIDDLE  ALT=\"dv%2Fdx=12x%5E2-82x%2B93.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >------derivative---BUT NOT NECESSARY....(?)\r<BR>\n" );
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document.write( "Extremes in volume would occur at  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%2882%2B-+sqrt%2882%5E2-4%2A12%2A93.5%29%29%2F%282%2A12%29 ALIGN=MIDDLE  ALT=\"x=%2882%2B-+sqrt%2882%5E2-4%2A12%2A93.5%29%29%2F%282%2A12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%2882%2B-+sqrt%282236%29%29%2F%282%2A12%29 ALIGN=MIDDLE  ALT=\"x=%2882%2B-+sqrt%282236%29%29%2F%282%2A12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%2841%2B-+sqrt%28559%29%29%2F12 ALIGN=MIDDLE  ALT=\"x=%2841%2B-+sqrt%28559%29%29%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "These are 1.446 and 5.387.  The larger of these makes no sense for the dimension of the paper.  The 1.446 has some meaning.  You could try second derivative to help check if this is a max or a min.\r<BR>\n" );
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document.write( "If you are allowed a graph tool,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-2%2C10%2C-2%2C40%2C4x%5E3-41x%5E2%2B93.5x%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-2%2C10%2C-2%2C40%2C4x%5E3-41x%5E2%2B93.5x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This looks like cut 1.446 inches at the corners will give the MAXIMUM volume. </SPAN>\n" );
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