document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=999604>Question 999604</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the 2 real numbers whose difference is 12 and whose product is as small as possible. Justify your answer using the 1st or 2nd derivative test. \r<BR>\n" );
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document.write( "Please explain<BR>\n" );
document.write( "Thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #617209 by </B><A HREF=/tutors/aboutme.mpl?userid=fractalier><B>fractalier(6550)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=fractalier><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=fractalier><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=617209\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We need to minimize<BR>\n" );
document.write( "f(x)=x(12+x)=12x + x^2<BR>\n" );
document.write( "Set the derivative equal to zero and get<BR>\n" );
document.write( "f'(x) = 12 + 2x = 0<BR>\n" );
document.write( "and x = -6<BR>\n" );
document.write( "The second derivative is<BR>\n" );
document.write( "f''(x) = 2<BR>\n" );
document.write( "so you know it is a minimum.<BR>\n" );
document.write( "Thus the two numbers are<BR>\n" );
document.write( "-6 and 6, and the product is -36. </SPAN>\n" );
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