document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=999606>Question 999606</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the area of the largest rectangle that has two sides on the positive x-axis and the positive y-axis one vertex at the origin and one vertex on the curve y = e^(-x) \r<BR>\n" );
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document.write( "Please explain<BR>\n" );
document.write( "Thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #617190 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=617190\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The area of the rectangle would then be,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%28x%29=x%2Ae%5E%28-x%29 ALIGN=MIDDLE  ALT=\"A%28x%29=x%2Ae%5E%28-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "To find the maximum area, differentiate the area with respect to x.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dA%2Fdx=x%2A%28-e%5E%28-x%29%29%2Be%5E%28-x%29%2A1 ALIGN=MIDDLE  ALT=\"dA%2Fdx=x%2A%28-e%5E%28-x%29%29%2Be%5E%28-x%29%2A1\"   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=e%5E%28-x%29%281-x%29 ALIGN=MIDDLE  ALT=\"dA%2Fdx=e%5E%28-x%29%281-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Set the derivative equal to zero.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%28-x%29%281-x%29=0 ALIGN=MIDDLE  ALT=\"e%5E%28-x%29%281-x%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So the solution is,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1-x=0 ALIGN=MIDDLE  ALT=\"1-x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So the maximum area of the rectangle is,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bmax%5D=1%28e%5E%28-1%29%29 ALIGN=MIDDLE  ALT=\"A%5Bmax%5D=1%28e%5E%28-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bmax%5D=1%2Fe ALIGN=MIDDLE  ALT=\"A%5Bmax%5D=1%2Fe\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );