document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1126376>Question 1126376</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A box is formed by cutting squares from the four corners of a sheet of paper and folding up the sides<BR>\n" );
document.write( "A)Suppose the paper is 5\"-wide by 7\"-long.<BR>\n" );
document.write( "I)What is the maximum volume for the box?<BR>\n" );
document.write( "ii)What is the maximum volume for the box?<BR>\n" );
document.write( "B)Suppose we instead create the box from a 7\"-wide by 9\"-long sheet of paper.<BR>\n" );
document.write( "I)What is the maximum volume for this box?<BR>\n" );
document.write( "ii)What cutout length produces 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 #742798 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39620)</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=742798\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> ----<BR>\n" );
document.write( "A box is formed by cutting squares from the four corners of a sheet of paper and folding up the sides<BR>\n" );
document.write( "A)Suppose the paper is 5\"-wide by 7\"-long.<BR>\n" );
document.write( "I)What is the maximum volume for the box?<BR>\n" );
document.write( "ii)What is the maximum volume for the box?<BR>\n" );
document.write( "----\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "v, volume<BR>\n" );
document.write( "x, length of square to remove at each corner<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v=x%285-2x%29%287-2x%29 ALIGN=MIDDLE  ALT=\"v=x%285-2x%29%287-2x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=algebra ALIGN=MIDDLE  ALT=\"algebra\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=steps ALIGN=MIDDLE  ALT=\"steps\"   DISABLED_style= \"max-width:90%; height:auto;\" >,...<BR>\n" );
document.write( "...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v=4x%5E3-24x%5E2%2B35 ALIGN=MIDDLE  ALT=\"v=4x%5E3-24x%5E2%2B35\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Extreme values:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dv%2Fdx=12x%5E2-48x%2B35 ALIGN=MIDDLE  ALT=\"dv%2Fdx=12x%5E2-48x%2B35\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12x%5E2-48x%2B35=0 ALIGN=MIDDLE  ALT=\"12x%5E2-48x%2B35=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Using quadratic formula solution, x for extreme values for v may be<BR>\n" );
document.write( " x at  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2824%2B-+sqrt%2878%29%29%2F12 ALIGN=MIDDLE  ALT=\"%2824%2B-+sqrt%2878%29%29%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "One of these may work and the other one may not work.\r<BR>\n" );
document.write( "\n" );
document.write( ".\r<BR>\n" );
document.write( "\n" );
document.write( ".<BR>\n" );
document.write( "The PLUS form is no good.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The MINUS form should work, for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1.264 ALIGN=MIDDLE  ALT=\"x=1.264\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Find v at x=1.264.<BR>\n" );
document.write( "Max v, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2813.97%2Ainch%5E3%29 ALIGN=MIDDLE  ALT=\"highlight%2813.97%2Ainch%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );