document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=175741>Question 175741</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 2. Find two numbers whose difference is 14 and whose product is a minimum. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #130873 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=130873\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's call your two numbers, A and B.<BR>\n" );
document.write( "\"difference is 14\" <BR>\n" );
document.write( "1.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A-B=14 ALIGN=MIDDLE  ALT=\"A-B=14\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "\"product is a minimum\"<BR>\n" );
document.write( "2.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f=A%2AB ALIGN=MIDDLE  ALT=\"f=A%2AB\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We want to minimize f.<BR>\n" );
document.write( "First, substitute for A and make f only a function of B. <BR>\n" );
document.write( "1.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A-B=14 ALIGN=MIDDLE  ALT=\"A-B=14\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=14%2BB ALIGN=MIDDLE  ALT=\"A=14%2BB\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28B%29=%2814%2AB%29%2AB=14B%2BB%5E2 ALIGN=MIDDLE  ALT=\"f%28B%29=%2814%2AB%29%2AB=14B%2BB%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "To minimize, take the derivative wrt B and set it equal to 0.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=df%2FdB=14%2B2B=0 ALIGN=MIDDLE  ALT=\"df%2FdB=14%2B2B=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=-7 ALIGN=MIDDLE  ALT=\"B=-7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then from 1,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=14%2BB ALIGN=MIDDLE  ALT=\"A=14%2BB\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=14-7 ALIGN=MIDDLE  ALT=\"A=14-7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=7 ALIGN=MIDDLE  ALT=\"A=7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );