document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1090161>Question 1090161</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the minimum product of two numbers whose difference is 32&#8203;? What are the&#8203; numbers?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #704563 by </B><A HREF=/tutors/aboutme.mpl?userid=htmentor><B>htmentor(1343)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=htmentor><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=htmentor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=704563\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let the two numbers be x and y.<BR>\n" );
document.write( "Their difference is 32, so y - x = 32 -> y = 32 + x<BR>\n" );
document.write( "We want to minimize the product xy:<BR>\n" );
document.write( "P = xy = x(32+x) = x^2 + 32x<BR>\n" );
document.write( "P will be a minimum when the derivative is equal to zero.<BR>\n" );
document.write( "dP/dx = 0 = 2x + 32, or x = -16<BR>\n" );
document.write( "Thus y = 32 - 16 = 16<BR>\n" );
document.write( "So the two numbers are 16 and -16 and the minimum product is -16*16 = -256<BR>\n" );
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