document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1061339>Question 1061339</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An open box is made from a rectangular piece of material, 13 inches by 10.5 inches, by cutting equal squares  (let it's side is x)from each corner and turning up the side. <BR>\n" );
document.write( "1. What is the dimensions of the box that has the maximum volume (V max)<BR>\n" );
document.write( "2. What is the maximum volume of the box (V max) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #676127 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39618)</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=676127\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x be the edge length of each square to be cut.\r<BR>\n" );
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document.write( "v for volume, will be<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28v=x%2813-2x%29%2810.5-2x%29%29 ALIGN=MIDDLE  ALT=\"highlight%28v=x%2813-2x%29%2810.5-2x%29%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=v=4x%5E3-47x%5E2%2B136.5x ALIGN=MIDDLE  ALT=\"v=4x%5E3-47x%5E2%2B136.5x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Maximize v, by looking for local max value or values.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dv%2Fdt=highlight_green%2812x%5E2-94x%2B136.5=0%29 ALIGN=MIDDLE  ALT=\"dv%2Fdt=highlight_green%2812x%5E2-94x%2B136.5=0%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=%2894%2B-+sqrt%282284%29%29%2F%282%2A12%29 ALIGN=MIDDLE  ALT=\"x=%2894%2B-+sqrt%282284%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=highlight_green%28x=%2847%2B-+sqrt%28571%29%29%2F12%29 ALIGN=MIDDLE  ALT=\"highlight_green%28x=%2847%2B-+sqrt%28571%29%29%2F12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Two values to examine.  Which of them is a maximum?<BR>\n" );
document.write( "Will it work with the dimensions of the sheet that you are given?\r<BR>\n" );
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document.write( "The decimal approximations for those values to examine are 1.93 and 5.91.<BR>\n" );
document.write( "If you think about the basic shape to expect for a cubic equation, such as for your volume,<BR>\n" );
document.write( "the maximum value will be to the left of the minimum value for the volume function.<BR>\n" );
document.write( "Expect x=1.93 to be your answer.<BR>\n" );
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