document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=677368>Question 677368</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How can I find the answer to this? Find two positive numbers' largest product if the first number plus twice the second number is equal to 48. I think I am supposed to use the first and second derivatives, but I'm not sure how to set it up!  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #420863 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=420863\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE p_1\"> represent the first number, and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE p_2\"> represent the second number, then\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \ p_1\ +\ 2p_2\ =\ 48\">\r<BR>\n" );
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document.write( "Hence, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE p_1\ =\ 48\ -\ 2p_2\">\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE y\ =\ p_2(48\ -\ 2p_2)\ =\ -(2p_2)^2\ -\ 48p_2\">\r<BR>\n" );
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document.write( "Take the first derivative, set it equal to zero.  Solve to get the ordinate of the extreme point.\r<BR>\n" );
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document.write( "Take the second derivative and evaluate it at the ordinate of the extreme point.  If positive, the extreme is a minimum, if negative, the extreme is a maximum.<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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