document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=199658>Question 199658</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the equation of the tangent to the curve defined by y=x-(e^-x) that is parallel to the line represented by 3x-y-9=0.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #150039 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=150039\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  Find the equation of the tangent to the curve defined by y=x-(e^-x) that is parallel to the line represented by 3x-y-9=0.<BR>\n" );
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document.write( "The slope, m, is 3.<BR>\n" );
document.write( "dy/dx = 3 = 1 + e^(-x)<BR>\n" );
document.write( "e^(-x) = 2<BR>\n" );
document.write( "-x = ln(2)<BR>\n" );
document.write( "x = -ln(2)<BR>\n" );
document.write( "y = -ln(2) - 2 = ~ -2.693147<BR>\n" );
document.write( "The tangent point is (-ln(2),-ln(2)-2)<BR>\n" );
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document.write( "y+ln(2)+2 = 3*(x+ln(2))<BR>\n" );
document.write( "y+ln(2)+2 = 3x+3ln(2)<BR>\n" );
document.write( "y = 3x + 2ln(2) - 2<BR>\n" );
document.write( "y = 3x - 0.6137 </SPAN>\n" );
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