document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=677470>Question 677470</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the dimensions that give the largest area for the rectangle. Its base is on the x-axis and its other two vertices are above the x-axis, lying on the parabola y=8-x^2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #420892 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=420892\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the dimensions that give the largest area for the rectangle. Its base is on the x-axis and its other two vertices are above the x-axis, lying on the parabola y=8-x^2<BR>\n" );
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document.write( "It's symmetrical about the y-axis, so find the max area on the + side.<BR>\n" );
document.write( "Area = x*y = x*(8-x^2) = 8x - x^3<BR>\n" );
document.write( "dA/dx = 8 - 3x^2 = 0<BR>\n" );
document.write( "x = sqrt(8/3) = 2sqrt(6)/3<BR>\n" );
document.write( "--> y = 16/3<BR>\n" );
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document.write( "Whole rectangle is 4sqrt(6)/3 by 16/3<BR>\n" );
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