document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=954959>Question 954959</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A rectangle has one vertex in quadrant 1 on the graph of y=16-x^2, another at the origin, one on the positive x-axis, and one on the positive y-axis.\r<BR>\n" );
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document.write( "Express the area A of the rectangle as a function of x. <BR>\n" );
document.write( "My answer: A(x)= 16x-x^3\r<BR>\n" );
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document.write( "Find the largest area A that can be enclosed by the rectangle? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #583340 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=583340\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The area of the rectangle would be,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=x%2Ay ALIGN=MIDDLE  ALT=\"A=x%2Ay\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=x%2816-x%5E2%29 ALIGN=MIDDLE  ALT=\"A=x%2816-x%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=A=16x-x%5E3 ALIGN=MIDDLE  ALT=\"A=16x-x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So far you are correct.<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "To find the maximum, take the derivative with respect to x and solve when the derivative equals zero.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dA%2Fdx=16-3x%5E2=0 ALIGN=MIDDLE  ALT=\"dA%2Fdx=16-3x%5E2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2=16 ALIGN=MIDDLE  ALT=\"3x%5E2=16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=16%2F3 ALIGN=MIDDLE  ALT=\"x%5E2=16%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4%2Fsqrt%283%29 ALIGN=MIDDLE  ALT=\"x=4%2Fsqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%284%2F3%29sqrt%283%29 ALIGN=MIDDLE  ALT=\"x=%284%2F3%29sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So then,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bmax%5D=16%284%2F3%29sqrt%283%29-%2816%2F3%29%284%2F3%29sqrt%283%29 ALIGN=MIDDLE  ALT=\"A%5Bmax%5D=16%284%2F3%29sqrt%283%29-%2816%2F3%29%284%2F3%29sqrt%283%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=%28128%2F9%29sqrt%283%29 ALIGN=MIDDLE  ALT=\"A%5Bmax%5D=%28128%2F9%29sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );