document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=382139>Question 382139</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find a positive number for which the sum of its reciprocal and four times its square is the smallest possible value. Show all work. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #270924 by </B><A HREF=/tutors/aboutme.mpl?userid=Jk22><B>Jk22(389)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Jk22><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=Jk22><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=270924\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Gives : 1/x+4x^2=f(x), f(x) has a minimum : <BR>\n" );
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document.write( "f'(x)=-1/x^2+8x=0 =>8x^3=1 => x=2<BR>\n" );
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document.write( "f''(x)=2/x^3+8 is >0 in x=2<BR>\n" );
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document.write( "hence the number is 2. </SPAN>\n" );
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