document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=3420>Question 3420</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find two positive real numbers whose sum is 40 and whose product is a maxium.<BR>\n" );
document.write( "Construct the function f(x) = x(40 - x).<BR>\n" );
document.write( "How is this found? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #1511 by </B><A HREF=/tutors/aboutme.mpl?userid=longjonsilver><B>longjonsilver(2297)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=longjonsilver><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=longjonsilver><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=1511\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let the 2 numbers be x and y.\r<BR>\n" );
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document.write( "so, we are told that x+y=40 --eqn1<BR>\n" );
document.write( "and that xy is to be a maximum.\r<BR>\n" );
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document.write( "so we have the function f(x) = xy. Now get rid of y by using eqn1 (written as y = 40-x... so f(x) = x(40-x)...easy enough?\r<BR>\n" );
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document.write( "We are told to find those 2 numbers that have the largest product (ie 1x39, 2x38, 3x37 etc)...\r<BR>\n" );
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document.write( "dy/dx = 40 - 2x = 0<BR>\n" );
document.write( "so, x=20<BR>\n" );
document.write( "so therefore, y must be 20 too\r<BR>\n" );
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document.write( "this is the answer: x=y=20\r<BR>\n" );
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document.write( "jon<BR>\n" );
document.write( " </SPAN>\n" );
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