document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1171489>Question 1171489</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the co ordinate turning point on the curve y=2e^4x +8e^-4x and determined the nature of the turning point  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #796630 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=796630\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> derivative is 8e^4x-32e^(-4x)<BR>\n" );
document.write( "set that equal to 0<BR>\n" );
document.write( "8e^4x=32 e^(-4x)<BR>\n" );
document.write( "e^4x=4/e^(4x)<BR>\n" );
document.write( "e^8x=4<BR>\n" );
document.write( "8x=ln4<BR>\n" );
document.write( "x=0.1733<BR>\n" );
document.write( "when y=8<BR>\n" );
document.write( "(0.1733, 8)<BR>\n" );
document.write( "-<BR>\n" );
document.write( "second derivative is 32e^4x-128e^(-4x); set that equal to 0<BR>\n" );
document.write( "e^4x=4/e^4x and we get a positive result, so this is a minimum.<BR>\n" );
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document.write( "</TD></TR></TABLE>\n" );