document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=889186>Question 889186</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Information: A rectangular box which is open at the top, has a square base with sides of x cm and a height of h cm.                               Question: An open rectangular box is to be constructed so that it can hold 256cm cube when completely full. What must its dimensions be so that as little material as possible is used in its construction?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #537975 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=537975\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Volume, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%2Ax%5E2=256 ALIGN=MIDDLE  ALT=\"h%2Ax%5E2=256\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Total one-sided area, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B4xh ALIGN=MIDDLE  ALT=\"x%5E2%2B4xh\"   DISABLED_style= \"max-width:90%; height:auto;\" >, represents the amount of material making the box.  A is the amount of material.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=x%5E2%2B4xh ALIGN=MIDDLE  ALT=\"A=x%5E2%2B4xh\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Solve the volume equation for h.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=256%2Fx%5E2 ALIGN=MIDDLE  ALT=\"h=256%2Fx%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and substitute into A equation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=x%5E2%2B4x%28256%2Fx%5E2%29 ALIGN=MIDDLE  ALT=\"A=x%5E2%2B4x%28256%2Fx%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28A=x%5E2%2B4%2A256%2Fx%29 ALIGN=MIDDLE  ALT=\"highlight%28A=x%5E2%2B4%2A256%2Fx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "The derivative way to continue for the minimum is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dA%2Fdx=0 ALIGN=MIDDLE  ALT=\"dA%2Fdx=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Not sure if you are studying Calculus so here is a try with just arithmetic.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=%28x%2Ax%5E2%2B4%2A256%29%2Fx ALIGN=MIDDLE  ALT=\"A=%28x%2Ax%5E2%2B4%2A256%29%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" >-----------No.  I am uncomfortable with this method.\r<BR>\n" );
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document.write( "DIFFENTIATING A:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dA%2Fdx=2x%2B%28-1%294%2A256%2Ax%5E%28-2%29 ALIGN=MIDDLE  ALT=\"dA%2Fdx=2x%2B%28-1%294%2A256%2Ax%5E%28-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dA%2Fdx=2x-4%2A256%2Fx%5E2 ALIGN=MIDDLE  ALT=\"dA%2Fdx=2x-4%2A256%2Fx%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%5E3-4%2A256%29%2Fx%5E2 ALIGN=MIDDLE  ALT=\"%282x%5E3-4%2A256%29%2Fx%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dA%2Fdx=0=2x%5E3-4%2A256 ALIGN=MIDDLE  ALT=\"dA%2Fdx=0=2x%5E3-4%2A256\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we only need to focus on the numerator to be zero.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E3=4%2A256 ALIGN=MIDDLE  ALT=\"2x%5E3=4%2A256\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3=2%2A256 ALIGN=MIDDLE  ALT=\"x%5E3=2%2A256\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=8%29 ALIGN=MIDDLE  ALT=\"highlight%28x=8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >----------assuming that this extreme will be for the minimum area.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=256%2F64 ALIGN=MIDDLE  ALT=\"h=256%2F64\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28h=4%29 ALIGN=MIDDLE  ALT=\"highlight%28h=4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >-----------the height dimension for this expected minimum material area.<BR>\n" );
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