document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1074408>Question 1074408</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Separate the number 14 into two parts such that the product of one part and the square of the other part is a maximum. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #689098 by </B><A HREF=/tutors/aboutme.mpl?userid=sachi><B>sachi(548)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=sachi><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=sachi><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=689098\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Separate the number 14 into two parts such that the product of one part and the square of the other part is a maximum.<BR>\n" );
document.write( "let one part is x <BR>\n" );
document.write( "so the other part is 14-x<BR>\n" );
document.write( "As per qn (14-x)x^2 is maximum<BR>\n" );
document.write( "now let f(x)=(14-x)x^2<BR>\n" );
document.write( "f'(x)=28x-3x^2<BR>\n" );
document.write( "for critical points f'(x)=0<BR>\n" );
document.write( "this gives x= 0 or 28/3<BR>\n" );
document.write( "now f\"(x)=28-6x<BR>\n" );
document.write( "so f\"(0)=28 >0<BR>\n" );
document.write( "& f\"(28/3)=-28 <0<BR>\n" );
document.write( "so for x=28/3 the f(x)is maximum<BR>\n" );
document.write( "so one part is 28/3 & the other part is 14/3<BR>\n" );
document.write( "ans </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );